NEET Electrostatic Potential and Capacitance — Set 11

Question 1

Two charges $ 15 \, \mu\text{C} $ and $ -5 \, \mu\text{C} $ are placed 12 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} $).

Accepted Answer

$ U = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r} = 9 \times 10^9 \times \frac{15 \times 10^{-6} \times (-5 \times 10^{-6})}{0.12} $. $ U = 9 \times 10^9 \times \frac{-75 \times 10^{-12}}{0.12} = -5.625 \, \text{J} $.

Question 2

A parallel plate capacitor with $ C = 50 \, \text{pF} $ in air has a dielectric ($ K = 4 $) inserted fully between plates. What is the new capacitance?

Accepted Answer

$ C' = K C = 4 \times 50 = 200 \, \text{pF} $.

Question 3

Why does the electric field inside the dielectric of a parallel plate capacitor decrease when the dielectric is inserted while keeping the plates disconnected?

Accepted Answer

When a dielectric ($ K > 1 $) is inserted into a disconnected capacitor, the charge $ Q $ remains constant. The dielectric polarizes, creating an induced field opposing the applied field. The effective field inside the dielectric becomes $ E = \frac{E_0}{K} $, where $ E_0 = \frac{\sigma}{\varepsilon_0} $ is the field without the dielectric ($ \sigma = Q/A $). Since $ K > 1 $, the field decreases due to the polarization reducing the net field between the plates.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 11

Q1. Two charges \( 15 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are placed 12 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q2. A parallel plate capacitor with \( C = 50 \, \text{pF} \) in air has a dielectric (\( K = 4 \)) inserted fully between plates. What is the new capacitance?

Q3. Why does the electric field inside the dielectric of a parallel plate capacitor decrease when the dielectric is inserted while keeping the plates disconnected?

Q4. A spherical conductor of radius 10 cm has a charge of \( 2 \times 10^{-7} \, \text{C} \). What is the electric field at a point 15 cm from its center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q5. Four capacitors of \( 25 \, \mu\text{F} \) each are in series. What is the equivalent capacitance?

Q6. A \( 7 \, \mu\text{F} \) capacitor is charged to \( 400 \, \text{V} \). What is the energy stored in it?

Q7. Two capacitors of \( 20 \, \text{pF} \) and \( 30 \, \text{pF} \) are connected in series. What is the equivalent capacitance?

Q8. In a system where a charged conductor is placed inside a larger uncharged hollow conductor, why does the inner conductor induce charges on both the inner and outer surfaces of the outer conductor?

Q9. Why does the capacitance of a parallel plate capacitor increase when the plates are moved closer while maintaining the same dielectric?

Q10. A dipole \( p = 3 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 0^\circ \) to \( 180^\circ \) in a field \( E = 4 \times 10^5 \, \text{N/C} \). What is the work done?