NEET Electrostatic Potential and Capacitance — Set 3

Question 1

A spherical conductor of radius 8 cm has a charge of $ 4 \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{4 \times 10^{-8}}{0.08} = 9 \times 10^9 \times 5 \times 10^{-7} = 4500 \, \text{V} $.

Question 2

Four charges $ +q, -q, +q, -q $ are at the corners of a square of side $ 2 \, \text{m} $ in order. What is the potential at the center? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $, $ q = 1 \, \mu\text{C} $).

Accepted Answer

Distance from center to each corner = $ \sqrt{2} \, \text{m} $. $ V = 9 \times 10^9 \left( \frac{1 \times 10^{-6}}{\sqrt{2}} + \frac{-1 \times 10^{-6}}{\sqrt{2}} + \frac{1 \times 10^{-6}}{\sqrt{2}} + \frac{-1 \times 10^{-6}}{\sqrt{2}} \right) = 0 \, \text{V} $.

Question 3

In a system of two identical charged spheres brought close together, why does the potential at the midpoint differ from the sum of their individual potentials?

Accepted Answer

The potential at a point due to multiple charges is the algebraic sum of the potentials due to each charge (principle of superposition). However, when two charged spheres are close, they influence each other’s charge distribution (mutual interaction), polarizing each other. This alters the effective potential at the midpoint compared to the sum of their individual potentials calculated in isolation, as the fields overlap and the charge distribution deviates from that of isolated spheres.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 3

Q1. A spherical conductor of radius 8 cm has a charge of \( 4 \times 10^{-8} \, \text{C} \). What is the potential at its surface? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q2. Four charges \( +q, -q, +q, -q \) are at the corners of a square of side \( 2 \, \text{m} \) in order. What is the potential at the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \), \( q = 1 \, \mu\text{C} \)).

Q3. In a system of two identical charged spheres brought close together, why does the potential at the midpoint differ from the sum of their individual potentials?

Q4. A \( 10 \, \mu\text{F} \) capacitor charged to \( 60 \, \text{V} \) is connected to an uncharged \( 30 \, \mu\text{F} \) capacitor. What is the energy lost?

Q5. A point charge \( Q = 2 \times 10^{-6} \, \text{C} \) is placed at the origin. What is the electrostatic potential at a point \( P \) located at \( (3, 4, 0) \, \text{m} \) from the origin? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q6. A dipole with \( p = 2 \times 10^{-9} \, \text{C m} \) makes an angle of \( 45^\circ \) with a uniform field \( E = 4 \times 10^5 \, \text{N/C} \). What is its potential energy?

Q7. In a system where a charged conductor is placed near an uncharged conductor, why does the uncharged conductor experience a net attractive force?

Q8. A \( 6 \, \mu\text{F} \) capacitor charged to \( 100 \, \text{V} \) is connected to an uncharged \( 6 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q9. A spherical conductor of radius 5 cm is charged with \( 3 \times 10^{-8} \, \text{C} \). What is the potential at its surface? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q10. Five capacitors of \( 30 \, \mu\text{F} \) each are in series. What is the equivalent capacitance?