Answer – According to the question, we have – Maximum Amplitude; \[{{A}_{max~}}\] = 10 V Minimum Amplitude; \[{{A}_{min}}~\]= 2 V It is quite known that the modulation index of an amplitude...
A carrier wave of peak voltage 12 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%?
Answer – 9V Explanation – We are given – Amplitude of carrier wave ; \[{{A}_{c}}\] = 12 V Modulation index (m) = 75% = 0.75 Amplitude of the modulating wave = ${{A}_{m}}$ We will now use the...
Define enzymes. Briefly describe the mechanism of enzyme catalysis.
Enzymes are large protein molecules with a high molecular mass. When they are dissolved in water, colloidal solutions are created. Living plants and animals manufacture these complex nitrogenous...
Digital signals
(i) Do not provide a continuous set of values (ii) Represent value as discrete steps (iii) Can utilize binary system (iv) Can utilize decimal as well as binary systems State which statement(s) are...
Write the differences between multimolecular and macromolecular colloids. Give one example of each. How are associated colloids different from these colloids.
(I) The colloidal particles in multi-molecular colloids are an assemblage of atoms or tiny molecules having a diameter of less than 1 nm. The molecules in the aggregate are held together by Van der...
Define lyophilic and lyophobic sols. Give one example of each type. Why are hydrophobic sols easily coagulated?
Lyophilic sols - Lyophilic sols are colloidal sols made by combining ingredients like gum, gelatin, starch, and others in a liquid called the dispersion medium. These sols are reversible in nature....
Discuss the trends in chemical reactivity of group 15 elements.
The general trends in chemical properties of the group – 15 are as follows:(i) Reactivity towards hydrogen:The elements present in group 15 undergo a reaction with hydrogen to form hydrides of type...
How do pressure and temperature affect the adsorption of gases on solids?
Effect of pressure : Because adsorption is a reversible process that is accompanied by a decrease in pressure, adsorption increases as pressure rises. Effect of temperature : According to...
Write the classification of colloidal solutions on the basis of physical states of the dispersed phase and dispersion medium.
Colloidal solutions can be classified as follows on the basis of their dispersed phase and dispersion medium : Dispersed phase Dispersion medium Type of colloid Example 1. Solid Solid Solid Sol...
Why is adsorption an exothermic process?
The process of adsorption is always exothermic. There are two ways to understand this which are as follows :- (I) The residual forces on the adsorbent's surface are reduced as a result of...
What is the role of adsorption in heterogeneous catalysis?
Heterogeneous catalysis is a catalytic process in which the catalyst and reactants are present in different phases. This form of heterogeneous catalytic action is explained by the adsorption theory....
What is the activation of adsorbent? How is it achieved?
Activation of adsorbent is the process of increasing the adsorption power of the adsorbent. The following methods are used to activate adsorbents: (I) Increasing the adsorbent surface area. This can...
What is an adsorption isotherm? Describe Freundlich’s adsorption isotherm.
The plot of the amount of adsorption (x/m) against the pressure of the gas (P) at constant temperature is known as the adsorption isotherm (T). Three cases arise from the graph which are as follow...
Frequencies in the UHF range normally propagate by means of :
(1) Ground Waves (2) Sky Waves (3) Surface Waves (4) Space Waves ANSWER – Space Waves Explanation – An ultra-high frequency (UHF) wave cannot be reflected back by the ionosphere as the highly...
Write the factors influencing the adsorption of a gas on a solid.
Factors influencing the adsorption of gas on a solid:- (1) Nature of the gas : Easily liquefiable gases, such as NH3, HCl, etc., have strong Van der Waal forces, so they are adsorbed to a greater...
Which of the following frequencies will be suitable for beyond-the horizon communication using sky waves?
(1) 10 kHz (2) 10 MHz (3) 1 GHz (4) 1000 GHz Answer - 10 MHz In case of beyond – the – horizon communication, the signal needs to cover large distances. For a signal of frequency 10kHz, the signal...
Why is a finely divided substance more effective as an adsorbent?
Because adsorption is a surface phenomenon, it is directly proportional to the surface area. Due to its large surface area, a finely split material acts as a good adsorbent. With an increase in...
Write at least 5 differences between physisorption and chemisorption.
Physisorption Chemisorption The adsorbate attaches to the surface of the adsorbent by weak van der Waal’s forces of attraction. The adsorbate...
Write the difference between absorption and adsorption illustrating using one example of each.
Absorption is the phenomenon of uniform distribution of a substance throughout the bulk of the solid and liquid. It is a bulk phenomenon. For example, absorption of water into the bulk of a sponge....
Why does the reactivity of nitrogen differ from phosphorus?
Nitrogen is a chemically less reactive element because of the high stability of its molecular form ${{N}_{2}}$. In nitrogen molecule, the two nitrogen atoms form a triple bond among themselves....
Discuss the general characteristics of Group 15 elements with reference to their electronic configuration, oxidation state, atomic size, ionisation enthalpy and electronegativity.
The general trend in group 15 elements is described as follows:(i) Oxidation states: The group 15 elements require 3 or more number of electrons to complete their octet and have 5 electrons in...
Write critical notes on the following:
(a) Eutrophication
(b) Biological magnification
(c) Groundwater depletion and ways for its replenishment
Solution: (a) Eutrophication – It is the natural aging process of a lake induced by nutrient enrichment caused by the influx of nutrients such as fertilizers, animal wastes, and sewage from land,...
With a neat, labelled diagram, describe the parts of a typical angiosperm ovule.
Solution: An ovule is a female megasporangium from where megaspores formation takes place. The various parts of an ovule are –1) Funicle - It is a stalk-like structure that serves as the point of...
With a neat diagram, explain the 7-celled, 8 nucleate natures of female gametophyte.
Solution: The mitotic division (reduction division) of the mother megaspore gives rise to female gametophytes. The megaspore divides mitotically thrice to form firstly 2 then 4 and out of these 4...
With a neat, labeled diagram, describe the parts of a typical angiosperm ovule.
Solution: An ovule is a female megasporangium from where megaspores formation takes place. The various parts of an ovule are –1) Funicle - It is a stalk-like structure that serves as the point of...
List any three important characteristics of a population and explain.
Solution: A population is a group of creatures belonging to the same species that live in a specific geographical area at a specified time and work together as a unit. The population of humans, for...
Select the statement which explains the best parasitism.
(a) One organism is benefited.
(b) Both the organisms are benefited.
(c) One organism is benefited, other is not affected.
(d) One organism is benefited, other is affected.
Solution: (d) One creature benefits, while the other is affected. Parasitism is a sort of interspecies interaction in which one species (parasite) benefits while the other species (host) suffers...
With the help of suitable diagram describe the logistic population growth curve.
Solution: The logistic population growth curve is most commonly observed in yeast cells produced in laboratory circumstances, and it contains five phases: The lag phase - the population of yeast...
Define the following terms and give one example for each:
(a) Commensalism
(b) Parasitism
(c) Camouflage
(d) Mutualism
(e) Interspecific competition
Solution: (a) Commensalism Commensalism is the interaction between two species in which one benefits while the other stays unaffected. Barnacles adhering to a whale's body and an orchid growing on...
Define population and community.
Solution: A population is a collection of individuals of the same species living in a specific geographical area at the same time and acting as a unit. A community can be defined as a group of...
Give an example for:
(a) An endothermic animal
(b) An ectothermic animal
(c) An organism of benthic zone
Solution: Crows, sparrows, cranes, cows, rabbits, rats, etc. are examples of endothermic animals. Amphibians, sharks, frogs, snakes, tortoises, and lizards are examples of ectothermic animals....
List the various abiotic environmental factors.
Solution: Abiotic environmental factors are formed by all the non-living components of an ecosystem which includes the following: Temperature – It is one of the most important elements that vary...
Write a short note on
(a) Adaptations of desert plants and animals
(b) Adaptations of plants to water scarcity
(c) Behavioral adaptations in animals
(d) Importance of light to plants
(e) Effect of temperature or water scarcity and the adaptations of animals.
Solution: (a) Adaptations of desert plants and animals Desert plants: The blazing heat and shortage of water are two of the most severe conditions found in deserts. Desert plants have adapted to...
Distinguish between the following:
(a) Hibernation and Aestivation
(b) Ectotherms and Endotherms
Solution: The differences are as follows: (a) Hibernation and Aestivation HibernationAestivationWinter sleep, also known as hibernation, is a state of reduced activity exhibited in some organisms in...
What is the ecological principle behind the biological control method of managing pest insects?
Solution: The biological management approach of managing pest insects is based on the ecological principle of predation. Predation is the biological interaction between a predator and prey in which...
An orchid plant is growing on the branch of the mango tree. How do you describe this interaction between the orchid and the mango tree?
Solution: Epiphytes, often known as air plants, are organisms that grow on other plants. An orchid growing on the branch of a mango tree is an example of an epiphyte. Such plants get their nutrients...
Name important defense mechanisms in plants against herbivory.
Solution: A category of animals that feeds only on plants is known as herbivores and this state or condition is called herbivory. Plants have evolved mechanisms both chemical and morphological, to...
If a population growing exponentially double in size in 3 years, what is the intrinsic rate of increase (r) of the population?
Solution: If food resources are adequately available to individuals in a population, it grows exponentially. To estimate the exponential growth, we can use the integral form of exponential growth...
Discuss briefly the following:
(a) Greenhouse gases (b) Catalytic converter (c) Ultraviolet B Solution: The following are discussed briefly below- (a) Greenhouse gases The global increase in the average temperature of the Earth...
List the attributes that populations possess but not individuals.
Solution: The population can be defined as a group of entities belonging to the same species, residing in a specific geographical area at a particular time, which also functioning together as a...
Most living organisms cannot survive at a temperature above 45 degrees C. How are some microbes able to live in habitats with temperatures exceeding 100 degrees C?
Solution: Thermophiles or Archaebacteria are ancient forms of bacteria that are found in deep-sea hydrothermal vents and hot water springs. They are able to tolerate the high temperature, which...
What initiatives were taken for reducing vehicular air pollution in Delhi? Has air quality improved in Delhi?
Solution: Delhi is the fourth most polluted city in the world, according to a list of 41 cities. The use of fossil fuels contributes to Delhi's air pollution. Several steps have been taken to...
If a marine fish is placed in a freshwater aquarium, will the fish be able to survive? Why or why not?
Solution: The chances of survival of marine fish will reduce if placed in a freshwater aquarium as their bodies are accustomed to an environment with higher salt concentrations. In a freshwater...
How is diapause different from hibernation?
Solution: Diapause is a phase of suspended development in an insect, other invertebrates, or mammal embryo, to deal with undesirable conditions. Several species of Zooplankton and insects go through...
Discuss briefly the following:
(a) Radioactive wastes (b) Defunct ships and e-wastes (c) Municipal solid wastes Solution: The following topics are explained below- (a) Radioactive wastes These are the wastes produced when...
What measures, as an individual, would you take to reduce environmental pollution?
Solution: Listed below are some measures that can be taken to prevent environmental pollution: To reduce air pollution, clean and renewable energy sources such as biofuels and compressed natural gas...
Discuss the role of women and communities in the protection and conservation of forests.
Solution: The role of communities and women in protecting and conserving forests has been significant. (i) The Chipko Movement In 1974, the ladies of the hamlet in the Garhwal region of the...
Why does an ozone hole form over Antarctica? How will enhanced ultraviolet radiation affect us?
Solution: Antarctica has more ozone holes than the rest of the world. They are generated as the concentration of chlorine in the environment rises. Chlorine is largely released by...
Match the items given in columns A and B:
Column AColumn B(a) Catalytic converter(i) Particulate matter(b) Electrostatic precipitator(ii) Carbon monoxide and nitrogen oxides(c) Earmuffs(iii) High noise level(d) Landfills(iv) Solid wastes...
Discuss the causes and effects of global warming. What measures need to be taken to control global warming?
Solution: An increase in the average temperature of the surface of the earth is termed Global warming. It can be caused due to the following reasons: (i) Global warming is caused by a rise in the...
List all the wastes that you generate, at home, school, or during your trips to other places. Could you very easily reduce the generation of these wastes? Which would be difficult or rather impossible to reduce?
Solution: Yes, there is a simple way to limit the consumption of these wastes. This can be accomplished by reducing the use of plastics and substituting other materials. Paper waste may be reduced...
What is apomixis and what is its importance?
Solution: Apomixis is the process of seed formation, where the seed forms without the occurrence of fertilization. This is basically the process of meiosis and syngamy. It is of high importance and...
Explain the role of the tapetum in the formation of a pollen grain wall.
Solution: Tapetum is the innermost layer of microsporangium and plays an important role in the formation of pollen grain walls. It provides the required nourishment to the maturing pollen grains....
What are the various constituents of domestic sewage? Discuss the effects of sewage discharge on a river.
Solution: Domestic sewage is the waste generated by households, including waste from the toilet, kitchen, laundry, and other sources. It comprises disease-causing germs, suspended solids (clay,...
If one can induce parthenocarpy through the application of growth substances, which fruits would you select to induce parthenocarpy and why?
Solution: Parthenocarpy is a method, where fruits are developed without fertilization, and the fruits bear no seeds. This process is best suited for fruits that are devoid of seeds such as...
What is meant by emasculation? When and why does a plant breeder employ this technique?
Solution: Emasculation refers to the removal of stems from bisexual flowers which later matures and form anther. This is done in order to avoid self-pollination in the flowers. This technique is...
Why is apple called a false fruit? Which part of the flower forms the fruit?
Solution: A false fruit is one that is derived from some secondary parts like the floral part and not from the ovary. Apple is derived from the thalamus (secondary part) and is hence called a false...
Differentiate between: Epicotyl and hypocotyl, Coleoptile and coleorhiza, Integument and Testa, Perisperm and pericarp.
Solution: Epicotyl and hypocotyl EpicotylHypocotylHere the region of the embryo is above the cotyledon.Here the region of the embryo is below the cotyledon.Epicotyl terminates from the...
Why do you think zygote is dormant for some time in a fertilized ovule?
Solution: The zygote remains inactive into an embryo until a certain amount of endosperm is formed. It provides the necessary nutrition to the developing embryo. This endosperm is formed from the...
What is triple fusion? Where and how does it take place? Name the nuclei involved in triple fusion.
Solution: Triple fusion occurs when two polar nuclei and a sperm nucleus fuses within the embryo sac of flowering plants. The events that take place in triple fusion are; The pollen grains get...
What is the bagging technique? How is it helpful in a plant breeding programmed?
Solution: The bagging technique is helpful in the prevention of fertilization of stigma by any undesired pollen. This is done by covering the emasculated flower (a flower whose anther is removed is...
What is self-incompatibility? Why does self-pollination not lead to seed formation in self-incompatible species?
Solution: Self-incompatibility refers to a genetically controlled mechanism, where pollen grains are unable to completely grow on the stigma of the flower. This process prevents self-pollination and...
Mention two strategies evolved to prevent self-pollination in flowers.
Solution: The two strategies involved in preventing self-pollination in flowers are: Dichogamy – It refers to the production of male and female reproductive organs at different times. Occurs with...
Can you think of a situation where we deliberately want to make a species extinct? How would you justify it?
Yes, there has been such a situation in which various parasites and microorganisms may need to be eradicated from the earth. Scientists are working hard to eradicate this parasite as these insects...
The species diversity of plants (22 per cent) is much less than that of animals (72 per cent). What could be the explanations to how animals achieved greater diversification?
There is a significant difference in the percentage of plant species (22%) and animal species (72%). The reasons for this difference are, 1. Adapting of animals in changing environments for survival...
Among the ecosystem services are control of floods and soil erosion. How is this achieved by the biotic components of the ecosystem?
The ecosystem consists of two types of substances. They are the abiotic and the biotic elements. While the abiotic components are air, light, water, temperature, soil, etc., the biotic components...
What are sacred groves? What is their role in conservation?
The Sacred groves are known as the tracts of forest restored in the places of worship. These are found in the Western Ghats of Karnataka, Rajasthan, Maharashtra, Madhya Pradesh, and Meghalaya. These...
How is biodiversity important for ecosystem functioning?
Importance of Biodiversity: 1. An ecosystem is more stable when it has a high species diversity when compared to a low species diversity ecosystem. 2. Higher biodiversity causes the environment to...
What are the major causes of species losses in a geographical region?
Biodiversity is the diversity of species found in different ecosystems including the diversity observed in living species from various sources such as air, water and land. However, the world's...
What is the significance of the slope of regression in a species-area relationship?
The slope is very helpful in finding local habitat relationships. Analysis of the geographical relationship in the sub-regions reveals that the rates of recurrence slopes are the same regardless of...
Give three hypotheses for explaining why tropics show the greatest levels of species richness.
As tropical areas receive more solar energy compared to tropical areas, it leads to a higher variety and higher productivity 2. Tropical regions have minimal seasonal variations and low-density...
What are chasmogamous flowers? Can cross-pollination occur in cleistogamous flowers? Give reasons for your answer.
Solution: Chasmogamous flowers are flowers that have open petals such that the pollen and stigma (the reproductive organs) are exposed to allow cross-pollination. On top of that chasmogamous flowers...
What is meant by the monosporic development of female gametophytes?
Solution: Monosporic development is the development of a female gametophyte from a single functional megaspore. In angiosperms, a single diploid mother megaspore undergoes meiotic cell division ....
Arrange the following terms incorrect developmental sequence: Pollen grain, sporogenous tissue, microspore tetrad, pollen mother cell, male gametes.
Solution: The correct developmental sequence is: Sporogenous tissue → pollen mother cell → microspore tetrad → pollen grain → male gamete.When the microsporangium is in the developing stage, every...
Differentiate between microsporogenesis and megasporogenesis. Which type of cell division occurs during these events? Name the structures formed at the end of these two events.
Solution: The most important differences between microsporogenesis and megasporogenesis are discussed below: MicrosporogenesisMegasporogenesisIt is the process where a diploid microspore mother cell...
Name the parts of an angiosperm flower in which the development of male and female gametophyte takes place.
Solution: In angiosperms, the male gametes are developed from a microspore that is present inside the pollen grains. They are released from the anther. But on the other side, the female gametes are...
Suppose that the particle in Exercise is an electron projected with velocity . If E between the plates separated by is , where will the electron strike the upper plate?
Solution: Given: Velocity of the electron, $\mathrm{v}_{\mathrm{x}}=2.0 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}$ Separation between the plates, $d=0.5 \mathrm{~cm}=0.5 \times 10^{-2} \mathrm{~m}$...
a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart. Solution: a) Assume that the equilibrium is at a state of stability....
It is now established that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.
Solution: Given, the net charge of a proton is +e. The value +e can be got when $p=\left(\frac{2}{3}+\frac{2}{3}-\frac{1}{3}\right) e$ The net charge of a neutron is 0 . This can be got when...
Obtain the formula for the electric field due to a long thin wire of uniform linear charge density E without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]
Solution:Consider the case of a long thin wire with a uniform linear charge density of 0 to 1. At r from the middle C of the wire, a point P is marked on the wire. The electric field produced by the...
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is , where is the unit vector in the outward normal direction and is the surface charge density near the hole.
Solution: If we assume that the hole has been filled, then Gauss's formula may be used to calculate the electric field intensity at a location near to the surface of the conductor, where Flux,...
(a) A conductor A with a cavity as shown in Fig. (a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor. (b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. (b)]. (c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
Solution: (a) Within the conductor that encloses the hollow, a Gaussian surface is taken into consideration. Within the conductor, the electric field strength (E) will be 0, indicating that it is...
In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC–1 per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10–7 cm in the negative z-direction?
Answer: Total dipole moment of the system, p=q×dl=−10−7 cm The rate of increase of the magnitude of the electric field along the positive z-direction = 105 NC–1 per metre. The...
Which among the curves shown in Fig. cannot possibly represent electrostatic field lines?
Solution:a. In the first case, the field lines are not parallel to the conductor's surface. As a result, it does not correspond to electrostatic field lines at...
An oil drop of 12 excess electrons is held stationary under a constant electric field of (Millikan’s oil drop experiment). The density of the oil is Estimate the radius of the drop.
Solution: Given: Excess electron on an oil drop, $n=12$ Electric field intensity, $E=2.55 \times 10^{4} \mathrm{NC}^{-1}$ Density of oil, $\rho=1.26 \mathrm{~g} \mathrm{~cm}^{-3}$ Acceleration due...
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude
What is E: (a) In the outer region of the first plate, (b) In the outer region of the second plate, and ( c) between the plates? Solution: As seen in the accompanying illustration, the scenario...
An infinite line charge produces a field of at a distance of Calculate the linear charge density.
Solution: The electric field produced by infinite line charges at a distance $d$ with linear charge density $\lambda$ is given by the relation, where is the distance in metres. $E=\frac{\lambda}{2...
A uniformly charged conducting sphere of diameter has a surface charge density of
(a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere? Solution: (a) Given: The diameter of the sphere, $d=2.4 \mathrm{~m}$ The radius of the...
A conducting sphere of radius has an unknown charge. If the electric field from the centre of the sphere is and points radially inward, what is the net charge on the sphere?
Solution: The strength of the electric field ( $E$ ) at a distance ( $d$ ) from the centre of a sphere holding net charge ( $q$ ) may be calculated using the following relationship: $E=\frac{1}{4...
A point charge causes an electric flux of to pass through a spherical Gaussian surface of radius centred on the charge.
(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge? Solution: (a)Given: Electric flux, $\Phi=-1.0 \times...
A point charge is at a distance directly above the centre of a square of side , as shown in Fig. 1.34. What is the magnitude of the electric flux through the square?
( Hint : Think of the square as one face of a cube with edge $10 \mathrm{~cm}$ ) Solution:One way to think of the square is as one of the faces of a cube with an edge and a centre where the charge...
Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is .
(a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?
Solutions: (a)Given: Net outward flux through the surface of the box, $\varphi=8.0 \times 10^{3} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{C}$ Concept: For a body containing net charge $q$, flux...
What is the net flux of the uniform electric field of Exercise through a cube of side oriented so that its faces are parallel to the coordinate planes?
Solution: The faces of a cube are all parallel to the coordinate axes on both sides of the object. So the number of field lines entering the cube is equal to the number of field lines piercing...
Consider a uniform electric field .
(a) What is the flux of this field through a square of $10 \mathrm{~cm}$ on a side whose plane is parallel to the y $z$ - plane? (b) What is the flux through the same square if the normal to its...
The figure below shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to the mass ratio?
We can see that particles 1 and 2 are traveling in the direction of the positive charge, and we know that opposing charges attract and identical charges repel. As a result, we may say that the...
Suppose the spheres A and B in Exercise 12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between and ?
Solution: Given: Distance between the spheres, $A$ and $B, r=0.5 \mathrm{~m}$ Initially, the charge on each of sphere $q=6.5 \times 10^{-7} C$ Concept and Calculation: When the sphere is contacted...
(i) Two insulated charged copper spheres A and B have their centers separated by a distance of . What is the mutual force of electrostatic repulsion if the charge on each is each? The radii of and are negligible compared to the distance of separation.
(ii) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
Solution: i) Given: Charge on sphere $\mathrm{A}, q_{A}=6.5 \times 10^{-7} C$ Charge on sphere $\mathrm{B}, q_{B}=6.5 \times 10^{-7} \mathrm{C}$ Distance between the spheres, $r=50 \mathrm{~cm}=0.5...
A polythene piece rubbed with wool is found to have a negative charge of
(i) Estimate the number of electrons transferred (from which to which?)
(ii) Is there a transfer of mass from wool to polythene?
Solution: (i) Because the wool is positively charged and the polythene is negatively charged, we can state that only a small number of electrons are transported from wool to polythene during the...
An electric dipole with dipole moment is aligned at with the direction of a uniform electric field of magnitude Calculate the magnitude of the torque acting on the dipole.
Solution: Given: Electric dipole moment, $p=4 \times 10^{-9} C m$ Angle made by $p$ with a uniform electric field, $\theta=30^{\circ}$ Electric field, $E=5 \times 10^{4} N C^{-1}$ Concept: Torque...
A system has two charges and located at points and , respectively. What is the total charge and electric dipole moment of the system?
Solution: Given: The charges which are located at the given points are shown in the co-ordinate system as At point $\mathrm{A}$, charge, $q_{A}=2.5 \times 10^{-7} C$ At point $B$, charge,...
Two-point charges qA = 3 µC and qB= –3 µC are located 20 cm apart in a vacuum.
(i) What is the electric field at the midpoint O of the line AB joining the two charges?
(ii) If a negative test charge of magnitude 1.5 × C is placed at this point, what is the force experienced by the test charge?
i) Given: Charges: qA = 3 µC qB= –3 µC Distance between them = 20 cm Diagrammatic representation of the above question is: Concept: An electric field is a physical field that surrounds...
i) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
(ii) Explain why two field lines never cross each other at any point. Answer: i) It is true that when a charge is placed in an electrostatic field, it will experience a constant force. As a result,...
Four-point charges are located at the corners of a square of side . What is the force on a charge of placed at the center of the square?
Solution: The square that was described in the inquiry is seen in the illustration above. Four charges are put in the corners of the squares on each side of the squares with a 10 cm side. And the...
When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
Answer: Whenever two bodies are rubbed against one other, a charge develops on both of the bodies involved. These charges are identical in magnitude but diametrically opposed in type. Charging by...
(i) Explain the meaning of the statement ‘electric charge of a body is quantized’.
(ii) Why can one ignore quantization of electric charge when dealing with macroscopic i.e., large-scale charges? Solution i) "It is quantized" in the sense that only integral (1,2,…. n) numbers of...
Check that the ratio is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
Solution: We know that the ratio to be determined is given as follows: $\frac{k e^{2}}{G m_{e} m_{p}}$ where $G$ is the gravitational constant in $N \mathrm{~m}^{2} \mathrm{~kg}^{-2}$ $m_{e}$ and...
The electrostatic force on a small sphere of charge due to another small sphere of charge in the air is .
(a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?
Solution: a. Given: The charge on $1^{\text {st }}$ sphere $\left(q_{1}\right)$ and $2^{\text {nd }}$ sphere $\left(q_{2}\right)$ is $0.4 \mu C$ or $0.4 \times 10^{-6} C$ and $-0.8 \times 10^{-6}...
What is the force between two small charged spheres having charges of and C placed apart in the air?
Solution: Given: The Charge on the $1^{\text {st }}$ sphere, $q_{1}=2 \times 10^{-7} \mathrm{C}$ The Charge on the $2^{\text {nd }}$ sphere, $q_{2}=3 \times 10^{-7} \mathrm{C}$ The distance...