NEET Electrostatic Potential and Capacitance — Set 20

Question 1

Two charges $ 5 \, \mu\text{C} $ and $ -5 \, \mu\text{C} $ are placed 10 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{5 \times 10^{-6} \times (-5 \times 10^{-6})}{0.1} = 9 \times 10^9 \times \frac{-25 \times 10^{-12}}{0.1} = -2.25 \, \text{J} $.

Question 2

An electric dipole with moment $ p = 7 \times 10^{-9} \, \text{C m} $ lies along the x-axis. What is the potential at $ (4, 0, 0) \, \text{m} $? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

Along the dipole axis ($ \theta = 0^\circ $): $ V = \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2} $. $ V = 9 \times 10^9 \times \frac{7 \times 10^{-9}}{4^2} = 9 \times 10^9 \times \frac{7 \times 10^{-9}}{16} = 3.9375 \, \text{V} $.

Question 3

A spherical conductor of radius 4 cm has a charge of $ 8 \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{8 \times 10^{-8}}{0.04} = 9 \times 10^9 \times 2 \times 10^{-6} = 18000 \, \text{V} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 20

Q1. Two charges \( 5 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are placed 10 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. An electric dipole with moment \( p = 7 \times 10^{-9} \, \text{C m} \) lies along the x-axis. What is the potential at \( (4, 0, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q3. A spherical conductor of radius 4 cm has a charge of \( 8 \times 10^{-8} \, \text{C} \). 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. An electric dipole with moment \( p = 3 \times 10^{-9} \, \text{C m} \) lies along the x-axis. What is the potential at \( (0, 5, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q5. A parallel plate capacitor with \( C = 80 \, \text{pF} \) in air has a dielectric (\( K = 8 \)) inserted fully between plates. What is the new capacitance?

Q6. A \( 5 \, \mu\text{F} \) capacitor charged to \( 200 \, \text{V} \) is connected to an uncharged \( 5 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q7. A spherical conductor of radius 3 cm has a charge of \( 3 \times 10^{-8} \, \text{C} \). What is the potential at its surface? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q8. A dipole \( p = 9 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 90^\circ \) to \( 180^\circ \) in a field \( E = 5 \times 10^4 \, \text{N/C} \). What is the work done?

Q9. A charged particle is placed in a region where the electric potential varies linearly with distance. What can be said about the electric field in that region?

Q10. A parallel plate capacitor with capacitance \( 300 \, \text{pF} \) has a dielectric (\( K = 3 \), thickness \( d/8 \)) inserted. What is the new capacitance? (Original separation \( d \)).