Physics

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.
β = √(n-1)k1 u/v / u + v

    i) Time taken by the ray to travel from S to P1 is = t1 = √u2 + b2/c Time taken by the ray to travel from P1 to O is = t2 = v/c (1+ ½ b2/v2) Time taken to travel through the lens is =...

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A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take L << |v-f|

The mirror formula is 1/v + 1/u = 1/f u is the object distance v is the image distance du = |u1 – u2| = L Differentiating on the both sides we get, dv/v2 = -du/u2 v/u = f/u-f du = L, therefore,...

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An astronomical refractive telescope has an objective of focal length 20m and an eyepiece of focal length 2cm.(a) The length of the telescope tube is 20.02m. (b) The magnification is 1000. (c) The image formed is inverted. (d) An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.

Answer: (a) The length of the telescope tube is 20.02m. (b) The magnification is 1000. (c) The image formed is inverted.                      ...

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A magnifying glass is used, as the object to be viewed can be brought closer to the eye than the normal near point. This results in
(a) a larger angle to be subtended by the object at the eye and hence viewed in greater detail.
(b) the formation of a virtual erect image.
(c) increase in the field of view.
(d) infinite magnification at the near point.

Answer: (a) a larger angle to be subtended by the object at the eye and hence viewed in greater detail. (b) the formation of a virtual erect image.              ...

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Between the primary and secondary rainbows, there is a dark band known as Alexandar’s dark band. This is because
(a) light scattered into this region interfere destructively.
(b) there is no light scattered into this region
(c) light is absorbed in this region.
(d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and 50°.

Answer: (a) light scattered into this region interfere destructively. (d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and...

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A rectangular block of glass ABCD has a refractive index 1.6. A pin is placed midway on the face AB. When observed from the face AD, the pin shall
(a) appear to be near A.
(b) appear to be near D.
(c) appear to be at the centre of AD.
(d) not be seen at all.

      Answer: (a) appear to be near A. (d) not be seen at all. The pin will appear to be near A as long as the angle of incidence on AD of the ray emerging from the pin is smaller...

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Consider an extended object immersed in water contained in a plane trough. When seen from close to the edge of the trough the object looks distorted because
(a) the apparent depth of the points close to the edge is nearer the surface of the water compared to the points away from the edge.
(b) the angle subtended by the image of the object at the eye is smaller than the actual angle subtended by the object in the air.
(c) some of the points of the object far away from the edge may not be visible because of total internal reflection.
(d) water in a trough acts as a lens and magnifies the object.

Answer: (a) the apparent depth of the points close to the edge is nearer the surface of the water compared to the points away from the edge. (b) the angle subtended by the image of the object at the...

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A car is moving with at a constant speed of 60 km h–1 on a straight road. Looking at the rearview mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h –1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 still the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?
(a) The speed of the car in the rear is 65 km h–1.
(b) In the side mirror, the car in the rear would appear to approach with a speed of 5 km h–1 to the driver of the leading car.
(c) In the rearview mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.
(d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

Answer: (d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

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The optical density of turpentine is higher than that of water while its mass density is lower. The figure shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in the figure, the path shown is correct?
a) 1
b) 2
c) 3
d) 4

              Answer: b) 2 When light travels from (optically) rarer medium air to optically denser medium turpentine, it bends towards the normal, i.e., θ1 >...

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The direction of a ray of light incident on a concave mirror as shown by PQ while directions in which the ray would travel after reflection is shown by four rays marked 1, 2, 3, and 4. Which of the four rays correctly shows the direction of reflected ray?
a) 1
b) 2
c) 3
d) 4

              Answer: b) 2 After reflection, the ray PQ of light that passes through focus F and strikes the concave mirror should become parallel to the primary...

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The phenomena involved in the reflection of radiowaves by ionosphere is similar to
a) reflection of light by a plane mirror
b) total internal reflection of light in the air during a mirage
c) dispersion of light by water molecules during the formation of a rainbow
d) scattering of light by the particles of air

Answer: b) total internal reflection of light in the air during a mirage The ionosphere, a layer of the atmosphere, reflects radio waves, allowing them to reach far-flung portions of the globe....

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The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will
a) act as a convex lens only for the objects that lie on its curved side
b) act as a concave lens only for the objects that lie on its curved side
c) act as a convex lens irrespective of the side on which the object lies
d) act as a concave lens irrespective of the side on which the object lies

Answer: c) act as a convex lens irrespective of the side on which the object lies

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A passenger in an aeroplane shall
a) never see a rainbow
b) may see a primary and a secondary rainbow as concentric circles
c) may see a primary and a secondary rainbow as concentric arcs
d) shall never see a secondary rainbow

Answer: b) may see a primary and a secondary rainbow as concentric circles As an aeroplane flies higher in the sky, passengers may notice a primary and secondary rainbow in the form of concentric...

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An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The image
a) moves away from the lens with a uniform speed 5 m/s
b) moves away from the lens with a uniform acceleration
c) moves away from the lens with a non-uniform acceleration
d) moves towards the lens with a non-uniform acceleration

Answer: c) moves away from the lens with a non-uniform acceleration In our case, the object approaches a convergent lens from the left at a uniform speed of 5 m/s, causing the image to travel away...

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Equipotential surfaces a) are closer in regions of large electric fields compared to regions of lower electric fields b) will be more crowded near sharp edges of a conductor c) will be more crowded near regions of large charge densities d) will always be equally spaced

The correct answer is a) are closer in regions of large electric fields compared to regions of lower electric fields b) will be more crowded near sharp edges of a conductor c) will be more crowded...

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A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d1 and dielectric constant k1 and the other has thickness d2 and dielectric constant k2 as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness d = d1 + d2 and effective dielectric constant k. The k is a) k1d1 + k2d2/d1+d2 b) k1d1 + k2d2/k1 + k2 c) k1k2 (d1 + d2)/(k1d1 + k2d2) d) 2k1k2/k1 + k2

The correct answer is c) k1k2 (d1 + d2)/(k1d1 + k2d2)

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The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statements are made in this regard: S1: At any point inside the sphere, the electric intensity is zero S2: At any point inside the sphere, the electrostatic potential is 100V Which of the following is a correct statement? a) S1 is true but S2 is false b) Both S1 and S2 are false c) S1 is true, S2 is also true, and S1 is the cause of S2 d) S1 is true, S2 is also true but the statements are independent

The correct answer is c) S1 is true, S2 is also true, and S1 is the cause of S2

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Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B. a) the work done in fig (i) is the greatest b) the work done in fig (ii) is least c) the work done is the same in fig (i), fig (ii), and fig (iii) d) the work done in fig (iii) is greater than fig (ii) but equal to that in fig (i)

The correct answer is c) the work done is the same in fig (i), fig (ii), and fig (iii)

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A positively charged particle is released from rest in a uniform electric field. The electric potential energy of the charge a) remains a constant because the electric field is uniform b) increases because the charge moves along the electric field c) decreases because the charge moves along the electric field d) decreases because the charge moves opposite to the electric field

The correct answer is c) decreases because the charge moves along the electric field

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In Young’s double slit experiment, the slits are 2mm apart and are illuminated by photons of two wavelength λ1 = 12000 Å and λ2 = 10000 Å. At what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Option A 3 mm Option B 8 mm Option C 6 mm Option D 4 mm Solution: The correct option is Option C Explanation: According to question, we have n1λ1 = n2λ2 $ \frac{{{\lambda }_{1}}}{{{\lambda...

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A 50 MHz sky wave takes 4.04 ms to reach a receiver via re-transmission from a satellite 600 km above earth’s surface. Assuming re-transmission time by satellite negligible, find the distance between source and receiver. If communication between the two was to be done by Line of Sight (LOS) method, what should size and placement of receiving and transmitting antenna be?

Answer: According to the question, the velocity of waves = 3 × 108 m/s The time to reach a receiver = 4.04 × 10-3 s we know that the height of satellite is: h = 600 km And the radius of earth = 6400...

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The maximum frequency for reflection of sky waves from a certain layer of the ionosphere is found to be f max = 9(Nmax) 1/2, where Nmax is the maximum electron density at that layer of the ionosphere. On a certain day, it is observed that signals of frequencies higher than 5MHz are not received by reflection from the F1 layer of the ionosphere while signals of frequencies higher than 8MHz are not received by reflection from the F2 layer of the ionosphere. Estimate the maximum electron densities of the F1 and F2 layers on that day.

Answer: Expression fpor the maximum frequency is: fmax = 9(Nmax)1/2 According to the question, for Layer F1, fmax = 5 MHz $ {{N}_{\max }}=\frac{F_{\max }^{2}}{9\times 9}=\frac{5\times...

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If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earths radius?

Answer: We know that the distance or range of transmission tower is given by the expression: $dT=\sqrt{2{{h}_{T}}R}$ R represents the radius of the earth (approximately 6400 km). hT​ denotes the...

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Two waves A and B of frequencies 2 MHz and 3 MHz, respectively are beamed in the same direction for communication via skywave. Which one of these is likely to travel a longer distance in the ionosphere before suffering total internal reflection?

Answer: The refractive index rises as the frequency rises, implying that the angle of refraction is smaller for higher frequency waves. In other words, bending is less. As a result, after covering a...

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A 1 KW signal is transmitted using a communication channel which provides attenuation at the rate of – 2dB per km. If the communication channel has a total length of 5 km, the power of the signal received is [gain in dB = 10 log P0/P1]

(a) 900 W (b) 100 W (c) 990 W (d) 1010 W Answer: The correct option is (b) 100 W Explanation: According to the question, Pi​ =1 kW = 1000W The rate of attenuation of the signal = -2dB/km Length of...

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Suppose a ‘n’-type wafer is created by doping Si crystal having 5 × 1028 atoms/m3 with 1ppm concentration of As. On the surface 200 ppm Boron is added to create the ‘P’ region in this wafer. Considering ni = 1.5 × 1016 m–3,

(i) Calculate the densities of the charge carriers in the n & p regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when the diode is reverse...

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A Zener of power rating 1 W is to be used as a voltage regulator. If Zener has a breakdown of 5V and it has to regulate voltage which fluctuated between 3V and 7V, what should be the value of Rs for safe operation in the figure?

Answer: According to the question, Power = 1W and Zener breakdown voltage = 5V We are given that the minimum voltage = 3V and the maximum voltage = 7V $ {{I}_{\max }}=\frac{P}{{{V}_{z}}}=\frac{1}{5}...

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Two car garages have a common gate which needs to open automatically when a car enters either of the garages or cars enter both. Devise a circuit that resembles this situation using diodes for this situation.

Answer: When an automobile approaches the gate, one or both gates are open. As a result, the OR gate produces the required result. The following is a truth table for the same: A B Y = A + B 0 0 0 0...

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In a CE transistor amplifier there is a current and voltage gain associated with the circuit. In other words, there is a power gain. Considering power a measure of energy, does the circuit violate conservation of energy?

Answer: The DC supply is connected to the CE transistor amplifier to provide energy to the signal. As a result, the CE configuration amplifier has a significant power gain. The extra power necessary...

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The amplifiers X, Y and Z are connected in series. If the voltage gains of X, Y and Z are 10, 20 and 30, respectively and the input signal is 1 mV peak value, then what is the output signal voltage (peak value)

(i) if dc supply voltage is 10V? (ii) if dc supply voltage is 5V? Answer: According to the question, we can write Voltage gain in X = vx = 10 Voltage gain in Y = vy = 20 Voltage gain in Z = vz = 30...

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The activity \mathrm{R} of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

    \[\begin{tabular}{|l|l|l|l|l|l|} \hline$t(\mathrm{~h})$ & 0 & 1 & 2 & 3 & 4 \\ \hline R(MBq) & 100 & $35.36$ & $12.51$ & $4.42$ & $1.56$ \\ \hline \end{tabular}\]


(i) Plot the graph of R versus t and calculate half-life from the graph.
(ii) Plot the graph of \ln \left(\mathrm{R} / \mathrm{R}_{0}\right) versus \mathrm{t} and obtain the value of half-life from the graph.

(i) Graph between $\mathrm{R}$ versus $\mathrm{t}$ will be an exponential curve. From the graph at slightly more than $\mathrm{t}=\frac{1}{2} \mathrm{~h}$ the $\mathrm{R}$ should be $50 \%$ so at...

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Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact:
(a) nuclear forces have short-range
(b) nuclei are positively charged
(c) the original nuclei must be completely ionized before fusion can take place
(d) the original nuclei must first break up before combining with each other

The correct options are: (a) nuclear forces have short-range (b) nuclei are positively charged

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A long straight cable of length I is placed symmetrically along the z-axis and has radius a. The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t)=I_{0} sin (2\pi vt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is \mathbf{E}(\mathrm{s}, \mathrm{t})=\mu_{0} \mathrm{l}_{0} \mathrm{~V} cos (2\pi vt). In \left(\frac{s}{a}\right) \hat{k},
a) calculate the displacement current density inside the cable
b) integrate the displacement current density across the cross-section of the cable to find the total displacement current I

a) The displacement current density is given as $\vec{J}_{d}=\frac{2 \pi I_{0}}{\lambda^{2}} \ln \frac{a}{s} \sin 2 \pi v t \hat{k}$ b) Total displacement current will be, $I^{d}=\int J_{d} 2 \pi s...

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What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant. What geometrical characteristics of the LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

When the distance between two points is doubled, the intensity of light is reduced by one-fourth. Geometrical characteristics of the LASER are: a) unidirectional b) monochromatic c) coherent...

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Electromagnetic waves with wavelength
i) \lambda_{1} is used in satellite communication
ii) \lambda_{2} is used to kill germs in water purifies
iii) \lambda_{3} is used to detect leakage of oil in underground pipelines
iv) \lambda_{4} is used to improve visibility in runaways during fog and mist conditions
a) identify and name the part of the electromagnetic spectrum to which these radiations belong
b) arrange these wavelengths in ascending order of their magnitude
c) write one more application of each

a) i) $\lambda_{1}$ is a microwave, used in satellite communication. ii) $\lambda_{2}$ is UV rays, used in a water purifier for killing germs. iii) $\lambda_{3}$ is X-rays, used in improving the...

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Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in the figure.A polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid (a) For a particular orientation, there shall be darkness as observed through the polaroid (b) The intensity of light as seen through the polaroid shall be independent of the rotation (c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid (d) The intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid

The correct answer is c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid

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In a Young’s double-slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there shall be alternate interference patterns of red and blue (b) there shall be an interference pattern for red distinct from that for blue (c) there shall be no interference fringes (d) there shall be an interference pattern for red mixing with one for blue

The correct answer is c) there shall be no interference fringes

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Two sources S1 and S2 of intensity I 1 and I 2 are placed in front of a screen in the figure (a). The pattern of intensity distribution seen in the central portion is given by the figure (b). In this case which of the following statements are true;(a) S1 and S2 have the same intensities (b) S1 and S2 have a constant phase difference (c) S1 and S2 have the same phase (d) S1 and S2 have the same wavelength.

The correct answer is a) S1 and S2 have the same intensities b) S1 and S2 have a constant phase difference c) S1 and S2 have the same phase

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(i) In the explanation of the photoelectric effect, we assume one photon of frequency ν collides with an electron and transfers its energy. This leads to the equation for the maximum energy Emax of the emitted electron as Emax = hν – φ0 where φ0 is the work function of the metal. If an electron absorbs 2 photons (each of frequency ν ) what will be the maximum energy for the emitted electron? (ii) Why is this fact (two-photon absorption) not taken into consideration in our discussion of the stopping potential?

i)According to the question, the electron absorbs two protons with frequencies of v and v'= 2v, where v' is the frequency of the released electron. Emax = hv – ϕ0 ii) There is no emission since the...

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Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber. Then (a) no electrons will be emitted as only photons can emit electrons (b) electrons can be emitted but all with an energy, E0 (c) electrons can be emitted with any energy, with a maximum of E0 – φ (φ is the work function) (d) electrons can be emitted with any energy, with a maximum of E0

The correct answer is d) electrons can be emitted with any energy, with a maximum of E0

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An electromagnetic wave travels in vacuum along z-direction: E=\left(E_{1} \hat{i}+E_{2} \hat{j}\right) \cos (k z-\omega t) \cdot Choose the correct options from the following:
a) the associated magnetic field is given as B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)
b) the associated magnetic field is given as B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)
c) the given electromagnetic field is circularly polarised
d) the given electromagnetic waves is plane polarised

a) the associated magnetic field is given as $B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)$ d) the given electromagnetic waves is plane polarised

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A multirange current meter can be constructed by using a galvanometer circuit shown in the figure. We want a current meter that can measure 10 mA, 100 mA, and 1 A using a galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find S1, S2, and S3 that have to be used.

I1 is measured as = 10 mA = IGG = (I1 – IG)(S1 + S2 + S3) I2 is measured as = 100 mA = IG(G+S1)=(I2-IG)(S2-S3) I3 is measured as = 1 A = IG(G+S1+S2)=(I3-IG)(S3) S1 = 1 Ω S2 = 0.1 Ω S3 = 0.01...

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Consider a circular current-carrying loop of radius R in the x-y plane with centre at the origin. Consider the line integral\Im (L)=\left| \left. \int_{-L}^{L}{B.dl} \right| \right.a) show that\Im (L)monotonically increases with L b) use an appropriate Amperian loop to that\Im (\infty )={{\mu }_{0}}Iwhere I is the current in the wire c) verify directly the above result d) suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about\Im (\infty )\text{and }\Im \text{(L)}

a) A circular current-carrying loop's magnetic field is given as \(\Im (L)=\int_{-L}^{+L}{Bdl}=2Bl\) It is a L function that increases monotonically. b) The Amperian loop is defined as follows:...

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A current-carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z, and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin.

The quarter's vector sum of the magnetic field at the origin is given as \({{\vec{B}}_{net}}=\frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)(\widehat{i}+\widehat{j}+\widehat{k})\)

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An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true? a) the electron will be accelerated along the axis b) the electron path will be circular about the axis c) the electron will experience a force at 45o to the axis and hence execute a helical path d) the electron will continue to move with uniform velocity along the axis of the solenoid

d) the electron will continue to move with uniform velocity along the axis of the solenoid

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The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of 11.3o with the axis of the earth. At Mumbai, declination is nearly zero. Then, a) the declination varies between 11.3o W to 11.3o E b) the least declination is 0o c) the plane defined by dipole axis and the earth axis passes through Greenwich d) declination average over the earth must be always negative

a) The declination ranges from 11.3 degrees West to 11.3 degrees East.

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A metallic ring of mass m and radius l (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of the magnetic field is Bz = Bo (1+λ z). If R is the resistance of the ring and if the ring falls with a velocity v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B, λ and acceleration due to gravity g.

v = mgR/B02π2λ2l4

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A circular coil expands radially in a region of the magnetic field and no electromotive force is produced in the coil. This can be because (a) the magnetic field is constant. (b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. (d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.

(b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is...

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There are two coils A and B. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that (a) there is a constant current in the clockwise direction in A. (b) there is a varying current in A. (c) there is no current in A. (d) there is a constant current in the counterclockwise direction in A.

(d) In A, there is a counterclockwise current that is constant.

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A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then (a) a direct current flows in the ammeter A. (b) no current flows through the ammeter A. (c) an alternating sinusoidal current flows through the ammeter A with a time period T=2π/ω. (d) a time-varying non-sinusoidal current flows through the ammeter A.

(b) There is no current flowing through ammeter A.

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