NEET Electrostatic Potential and Capacitance — Set 2

Question 1

In a system of two point charges of opposite signs placed close to each other, what can be said about the equipotential surface passing through the midpoint between them?

Accepted Answer

For two point charges of opposite signs ($ +q $ and $ -q $), the potential at the midpoint is zero (since $ V = \frac{q}{4 \pi \varepsilon_0 r} - \frac{q}{4 \pi \varepsilon_0 r} = 0 $, where $ r $ is the distance from each charge to the midpoint). The equipotential surface where $ V = 0 $ is the plane perpendicular to the line joining the charges, passing through the midpoint, as points on this plane equidistant from both charges have potentials that cancel out.

Question 2

Two capacitors $ 10 \, \mu\text{F} $ and $ 20 \, \mu\text{F} $ are in parallel. What is the total capacitance?

Accepted Answer

$ C = C_1 + C_2 = 10 + 20 = 30 \, \mu\text{F} $.

Question 3

A spherical conductor of radius 15 cm has a charge of $ 6 \times 10^{-8} \, \text{C} $. What is the electric field at 40 cm from the center? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

For $ r = 0.4 \, \text{m} > R = 0.15 \, \text{m} $, $ E = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r^2} $. $ E = 9 \times 10^9 \times \frac{6 \times 10^{-8}}{(0.4)^2} = 9 \times 10^9 \times \frac{6 \times 10^{-8}}{0.16} = 3.375 \times 10^3 \, \text{N/C} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 2

Q1. In a system of two point charges of opposite signs placed close to each other, what can be said about the equipotential surface passing through the midpoint between them?

Q2. Two capacitors \( 10 \, \mu\text{F} \) and \( 20 \, \mu\text{F} \) are in parallel. What is the total capacitance?

Q3. A spherical conductor of radius 15 cm has a charge of \( 6 \times 10^{-8} \, \text{C} \). What is the electric field at 40 cm from the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q4. A charge of \( 9 \, \mu\text{C} \) is moved from infinity to a point where the potential is \( 40 \, \text{V} \). What is the work done?

Q5. A \( 4 \, \mu\text{F} \) capacitor charged to \( 100 \, \text{V} \) is connected to an uncharged \( 4 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q6. In a parallel combination of capacitors, why does each capacitor have the same potential difference across its plates?

Q7. A positively charged particle moves from a point of higher potential to a point of lower potential in an electrostatic field. What is the sign of the work done by the electric field?

Q8. A parallel plate capacitor with capacitance \( 250 \, \text{pF} \) has a dielectric (\( K = 4 \), thickness \( d/7 \)) inserted. What is the new capacitance? (Original separation \( d \)).

Q9. Two hollow spherical conductors of different radii are charged with the same amount of charge and then connected by a thin conducting wire. What happens to the charges on the conductors?

Q10. A spherical conductor of radius 35 cm has a charge of \( 14 \times 10^{-8} \, \text{C} \). What is the electric field at 80 cm from the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).