# Blog

### Why does the electric field inside a dielectric decrease when it is placed in an external electric field?

Ans: The electric field that is present inside a dielectric decreases when it is placed in an external electric field because of polarisation as it creates an internal electric field which is...

### State Gauss’s Theorem in electrostatics? Using this theorem define an expression for the field intensity due to an infinite plane sheet of change of charge density .

Ans: Gauss's Theorem has a statement that electric flux through a closed surface enclosing a charge $q$ in vacuum is $\frac{1}{\epsilon_{0}}$ times the magnitude of the charge enclosed $\mathrm{is}...

### Prove that the energy stored in a parallel plate capacitor is given by

Ans: Let us suppose a capacitor is connected to a battery and it supplies a small amount of change dq at constant potential $V$, then a small amount of work done by the battery is given by $$...

### Two dielectric slabs of dielectric constant and are filled in between the two plates, each of area A of the parallel plate capacitor as shown in the figure. Find the net capacitance of the capacitor? Area of each plate

Ans: In the question, the two capacitors are in parallel Net Capacitance, $C=C_{1}+C_{2}$ $$ \begin{array}{l} \mathrm{C}_{1}=\frac{\mathrm{K}_{1}...

### Describe schematically the equipotential surfaces corresponding to a) a constant electric field in the z-direction,

Ans: Equidistant planes which are parallel to the $x-y$ plane are the equipotential surfaces. b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction, Ans:...

### In a Van de Graaff type generator a spherical metal shell is to be a electrode. The dielectric strength of the gas surrounding the electrode is . What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)

Ans: Given that, Potential difference is given as, $V=15 \times 10^{6} \mathrm{~V}$ Dielectric strength of the surrounding gas $=5 \times 10^{\top} \mathrm{Vm}^{-1}$ Electric field intensity is...

### Two charges and are placed at points and apart. a) Identify an equipotential surface of the system.

Ans: The situation is represented in the adjoining figure. An equipotential surface is the plane on which the total potential is zero everywhere. This plane is normal to line AB. The plane is...

### The distance between the plates of a parallel plate capacitor is d. A metal plate of thickness is placed between the plates. What will be the effect on the capacitance?

Ans: For air $C_{0}=\frac{A \in_{0}}{d}$ Thickness $t=\frac{d}{2}$ only when $k=\infty$ $$ \begin{array}{l} C_{0}=\frac{A \in_{0}}{d} \\ C_{\text {mat }}=\frac{A \in_{0}}{(d-t)} \end{array} $$ $$...

### A stream of electrons travelling with speed at right angles to a uniform electric field is deflected in a circular path of radius Prove that

Ans: The path of the electron that is travelling with velocity $\mathrm{vm} / \mathrm{s}$ at right angle of $\bar{E}$ is of circular shape. It requires a centripetal in nature, $F=\frac{m v^{2}}{r}$...

### If the amount of electric flux entering and leaving a closed surface are and respectively. What is the electric charge inside the surface?

Ans: Net flux can be given as $=\phi_{2}-\phi_{1}$ Since $\phi=\frac{q}{\epsilon_{0}}$ $$ \Rightarrow \mathrm{Q}=\left(\phi_{2}-\phi_{1}\right) \in_{0} $$ The electric charge inside the surface can...

### Draw one equipotential surfaces (1) Due to uniform electric field (2) For a point charge

Ans: The diagrams are given as: Equipoterhibil Surfaces 3 $\mathrm{~ ( 2 c ) r o m}$

### A parallel plate capacitor with air between the plates has a capacitance of 8pF . What will be the capacitance if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant 6 ?

Ans: For air, capacitance can be expressed as, $C_{0}=\frac{A \in_{0}}{d}$ $$ C_{0}=8 \times p F=8 \times 10^{-12} F $$ Now $d^{\prime}=\frac{d}{2}$ and $K=6$ $$ \begin{array}{l} \Rightarrow...