NEET Electrostatic Potential and Capacitance — Set 21

Question 1

A $ 8 \, \mu\text{F} $ capacitor is charged to $ 500 \, \text{V} $. What is the energy stored in it?

Accepted Answer

$ U = \frac{1}{2} C V^2 = \frac{1}{2} \times 8 \times 10^{-6} \times (500)^2 $. $ U = \frac{1}{2} \times 8 \times 10^{-6} \times 250000 = 1 \, \text{J} $.

Question 2

Why does the electric field inside a charged spherical shell vary linearly with distance from the center when a uniform dielectric fills the interior?

Accepted Answer

Electrostatic Potential and Capacitance typically assumes no charge inside a spherical shell, leading to $ E = 0 $. However, if misinterpreted as a charged dielectric sphere (common in advanced contexts but not in the PDF), the field varies as $ E \propto r $. Since the PDF context implies an empty shell or uniform shell charge, $ E = 0 $. Assuming a misinterpretation, the correct context is $ E = 0 $, but for a filled dielectric with uniform charge (not in PDF), $ E $ varies linearly. Here, we clarify: $ E = 0 $ inside a shell, so no variation.

Question 3

Why does the potential energy of a system of two charges depend only on their separation and not on their orientation in space?

Accepted Answer

The potential energy between two point charges is $ U = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r} $, where $ r $ is the distance between them. This expression depends only on the magnitude of the separation $ r $, not on the direction or orientation of the line joining the charges in space, because the Coulomb force is isotropic (depends only on distance) and the potential is a scalar quantity derived from integrating the force over distance, independent of spatial orientation.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 21

Q1. A \( 8 \, \mu\text{F} \) capacitor is charged to \( 500 \, \text{V} \). What is the energy stored in it?

Q2. Why does the electric field inside a charged spherical shell vary linearly with distance from the center when a uniform dielectric fills the interior?

Q3. Why does the potential energy of a system of two charges depend only on their separation and not on their orientation in space?

Q4. Two charges \( 6 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are at \( (10, 0, 0) \) and \( (-10, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q5. Three capacitors \( 8 \, \text{pF} \), \( 16 \, \text{pF} \), and \( 32 \, \text{pF} \) are in parallel. What is the total capacitance?

Q6. A \( 2 \, \mu\text{F} \) capacitor charged to \( 200 \, \text{V} \) loses how much energy when connected to an uncharged \( 3 \, \mu\text{F} \) capacitor?

Q8. Three capacitors \( 6 \, \text{pF} \), \( 12 \, \text{pF} \), and \( 4 \, \text{pF} \) are in series. What is the equivalent capacitance?

Q9. A \( 1 \, \mu\text{F} \) capacitor is charged to \( 400 \, \text{V} \). What is the energy stored in it?

Q10. When a dielectric slab is inserted between the plates of a charged parallel plate capacitor (disconnected from the battery), what happens to the energy stored in the capacitor?