NEET Electrostatic Potential and Capacitance — Set 24

Question 1

In an electrostatic field, if a positive charge is moved along an equipotential surface, what can be said about the work done by the electric field?

Accepted Answer

An equipotential surface has a constant potential at all points. The work done by the electric field when a charge moves along such a surface is zero because the potential difference between any two points on the surface is zero ($ W = q \Delta V $, and $ \Delta V = 0 $). Additionally, the electric field is always perpendicular to an equipotential surface, so there is no component of the field along the direction of motion, confirming that no work is done.

Question 2

When two identical capacitors, one charged and one uncharged, are connected in parallel, why does the total energy decrease even though charge is conserved?

Accepted Answer

When a charged capacitor ($ C $, charge $ Q $, voltage $ V $) is connected in parallel with an uncharged capacitor ($ C $), the total capacitance becomes $ 2C $, and the charge redistributes to a final voltage $ V' = Q/(2C) = V/2 $. Initial energy is $ U_i = \frac{Q^2}{2C} $, while final energy is $ U_f = \frac{(Q)^2}{2 \times 2C} = \frac{Q^2}{4C} $, which is half the initial energy. The decrease occurs because energy is lost as heat or radiation during the transient current flow when charges redistribute, even though charge is conserved.

Question 3

A point charge $ Q = 21 \times 10^{-9} \, \text{C} $ is placed at the origin. Calculate the potential at a point 7 m away from the charge. (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

Potential due to a point charge: $ V = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r} $. Substitute: $ V = 9 \times 10^9 \times \frac{21 \times 10^{-9}}{7} = 9 \times 10^9 \times 3 \times 10^{-9} = 27 \, \text{V} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 24

Q1. In an electrostatic field, if a positive charge is moved along an equipotential surface, what can be said about the work done by the electric field?

Q2. When two identical capacitors, one charged and one uncharged, are connected in parallel, why does the total energy decrease even though charge is conserved?

Q3. A point charge \( Q = 21 \times 10^{-9} \, \text{C} \) is placed at the origin. Calculate the potential at a point 7 m away from the charge. (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q4. A \( 5 \, \mu\text{F} \) capacitor is charged to \( 200 \, \text{V} \). What is the energy stored in it?

Q5. When a conductor is placed in an external electric field, why does the potential throughout its volume become constant in electrostatic equilibrium?

Q6. A point charge \( Q = 6 \times 10^{-9} \, \text{C} \) is placed at the origin. Calculate the potential at a point 2 m away from the charge. (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q7. Three capacitors \( 2 \, \text{pF} \), \( 4 \, \text{pF} \), and \( 8 \, \text{pF} \) are in parallel. What is the total capacitance?

Q8. A spherical conductor of radius 20 cm has a charge of \( 8 \times 10^{-8} \, \text{C} \). What is the electric field at 50 cm from the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q9. Why does the electric field due to an infinite charged sheet remain constant with distance from the sheet?

Q10. Two capacitors of \( 15 \, \text{pF} \) each are connected in series. What is the equivalent capacitance?