NEET Electrostatic Potential and Capacitance — Set 14

Question 1

A parallel plate capacitor with capacitance $ 50 \, \text{pF} $ has a dielectric ($ K = 2 $, thickness $ d/3 $) inserted. What is the new capacitance? (Original separation $ d $).

Accepted Answer

Potential difference: $ V = E_0 \left( \frac{2d}{3} \right) + \frac{E_0}{K} \left( \frac{d}{3} \right) = E_0 d \left( \frac{2}{3} + \frac{1}{3 \times 2} \right) = E_0 d \left( \frac{2}{3} + \frac{1}{6} \right) = E_0 d \times \frac{5}{6} $. $ C = \frac{Q}{V} = \frac{Q}{\frac{5}{6} V_0} = \frac{6}{5} \times 50 = 60 \, \text{pF} $.

Question 2

Why does the electric field inside a conductor vanish in electrostatic equilibrium, even if the conductor is irregularly shaped?

Accepted Answer

In electrostatic equilibrium, free charges in a conductor redistribute to cancel any internal electric field. If there were a field inside, it would exert a force on the free charges, causing them to move until the field becomes zero everywhere inside. This principle holds regardless of shape because conductors allow charge mobility, and equilibrium requires $ E = 0 $ inside, with all excess charge residing on the surface, adjusting to the geometry.

Question 3

Two charges $ 20 \, \mu\text{C} $ and $ -10 \, \mu\text{C} $ are at $ (1, 0, 0) $ and $ (-1, 0, 0) \, \text{cm} $. What is the potential at midpoint? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

Distance to midpoint = 0.01 m. $ V = 9 \times 10^9 \left( \frac{20 \times 10^{-6}}{0.01} + \frac{-10 \times 10^{-6}}{0.01} \right) = 9 \times 10^9 \times \frac{10 \times 10^{-6}}{0.01} $. $ V = 9 \times 10^9 \times \frac{10 \times 10^{-6}}{0.01} = 9 \times 10^6 \, \text{V} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 14

Q1. A parallel plate capacitor with capacitance \( 50 \, \text{pF} \) has a dielectric (\( K = 2 \), thickness \( d/3 \)) inserted. What is the new capacitance? (Original separation \( d \)).

Q2. Why does the electric field inside a conductor vanish in electrostatic equilibrium, even if the conductor is irregularly shaped?

Q3. Two charges \( 20 \, \mu\text{C} \) and \( -10 \, \mu\text{C} \) are at \( (1, 0, 0) \) and \( (-1, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q4. A parallel plate capacitor with capacitance \( 150 \, \text{pF} \) has a dielectric (\( K = 6 \), thickness \( d/5 \)) inserted. What is the new capacitance? (Original separation \( d \)).

Q5. A dipole \( p = 4 \times 10^{-10} \, \text{C m} \) is in a uniform field \( E = 10^5 \, \text{N/C} \) at \( 60^\circ \). What is its potential energy?

Q6. A parallel plate capacitor has plates of area \( 0.05 \, \text{m}^2 \) separated by 1 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q7. In an electrostatic shielding scenario, a cavity inside a conductor contains a charge. What can be said about the electric field outside the conductor?

Q8. Two charges \( 18 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) are placed 18 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q9. A charged particle is placed in a region where the electric potential is constant everywhere. What can be inferred about the motion of the particle if it is released from rest?

Q10. A dipole with \( p = 3 \times 10^{-9} \, \text{C m} \) makes an angle of \( 60^\circ \) with a uniform field \( E = 2 \times 10^5 \, \text{N/C} \). What is its potential energy?