NEET Electrostatic Potential and Capacitance — Set 23

Question 1

A parallel plate capacitor with $ A = 0.01 \, \text{m}^2 $, $ d = 1 \, \text{mm} $ has a dielectric ($ K = 5 $). What is its capacitance? (Take $ \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} $).

Accepted Answer

$ C = \frac{\varepsilon_0 K A}{d} = \frac{8.85 \times 10^{-12} \times 5 \times 0.01}{10^{-3}} = 4.425 \times 10^{-10} \, \text{F} = 442.5 \, \text{pF} $.

Question 2

A dipole $ p = 8 \times 10^{-10} \, \text{C m} $ is rotated from $ \theta = 0^\circ $ to $ 90^\circ $ in a field $ E = 10^6 \, \text{N/C} $. What is the work done?

Accepted Answer

Work done: $ W = p E (\cos \theta_0 - \cos \theta_1) = 8 \times 10^{-10} \times 10^6 \times (\cos 0^\circ - \cos 90^\circ) = 8 \times 10^{-4} \times (1 - 0) = 8 \times 10^{-4} \, \text{J} $.

Question 3

A spherical conductor of radius 5 cm has a charge of $ 5 \times 10^{-8} \, \text{C} $. What is the potential at its surface? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

Potential at the surface: $ V = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{R} $. $ V = 9 \times 10^9 \times \frac{5 \times 10^{-8}}{0.05} = 9 \times 10^9 \times 10^{-6} = 9000 \, \text{V} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 23

Q1. A parallel plate capacitor with \( A = 0.01 \, \text{m}^2 \), \( d = 1 \, \text{mm} \) has a dielectric (\( K = 5 \)). What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q2. A dipole \( p = 8 \times 10^{-10} \, \text{C m} \) is rotated from \( \theta = 0^\circ \) to \( 90^\circ \) in a field \( E = 10^6 \, \text{N/C} \). What is the work done?

Q3. A spherical conductor of radius 5 cm has a charge of \( 5 \times 10^{-8} \, \text{C} \). What is the potential at its surface? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q4. A \( 6 \, \mu\text{F} \) capacitor charged to \( 150 \, \text{V} \) is connected to an uncharged \( 9 \, \mu\text{F} \) capacitor. What is the energy lost?

Q5. A dipole with \( p = 5 \times 10^{-9} \, \text{C m} \) makes an angle of \( 30^\circ \) with a uniform field \( E = 3 \times 10^4 \, \text{N/C} \). What is its potential energy?

Q6. Why does the potential due to an electric dipole fall off as \( 1/r^2 \) at large distances, unlike the potential of a point charge which falls off as \( 1/r \)?

Q7. A \( 9 \, \mu\text{F} \) capacitor is charged to \( 600 \, \text{V} \). What is the energy stored in it?

Q8. Four capacitors of \( 5 \, \mu\text{F} \) each are in series. What is the equivalent capacitance?

Q9. When a dielectric slab fills only half the space between the plates of a parallel plate capacitor (connected to a battery), why does the electric field differ in the dielectric and air regions?

Q10. An electric dipole with moment \( p = 10^{-9} \, \text{C m} \) lies along the y-axis. What is the potential at \( (0, 3, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).