NEET Electrostatic Potential and Capacitance — Set 7

Question 1

Three charges $ +8 \, \mu\text{C} $, $ -5 \, \mu\text{C} $, and $ +3 \, \mu\text{C} $ are at $ (0, 0, 0) $, $ (8, 0, 0) $, and $ (0, 8, 0) \, \text{m} $. What is the potential at $ (8, 8, 0) \, \text{m} $? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

Distances: $ r_1 = \sqrt{8^2 + 8^2} = 8\sqrt{2} \, \text{m} $, $ r_2 = 8 \, \text{m} $, $ r_3 = 8 \, \text{m} $. $ V = 9 \times 10^9 \left( \frac{8 \times 10^{-6}}{8\sqrt{2}} + \frac{-5 \times 10^{-6}}{8} + \frac{3 \times 10^{-6}}{8} \right) $. $ V = 9 \times 10^9 \left( \frac{8 \times 10^{-6}}{11.314} - \frac{5 \times 10^{-6}}{8} + \frac{3 \times 10^{-6}}{8} \right) $. $ V = 9 \times 10^9 \left( 0.707 \times 10^{-6} - 0.625 \times 10^{-6} + 0.375 \times 10^{-6} \right) $. $ V = 9 \times 10^9 \times 0.457 \times 10^{-6} = 4113 \, \text{V} $.

Question 2

A $ 16 \, \mu\text{F} $ capacitor charged to $ 10 \, \text{V} $ is connected to an uncharged $ 16 \, \mu\text{F} $ capacitor. What is the final potential difference?

Accepted Answer

Initial charge: $ Q = 16 \times 10^{-6} \times 10 = 1.6 \times 10^{-4} \, \text{C} $. Total capacitance: $ 16 + 16 = 32 \, \mu\text{F} $. Final voltage: $ V = \frac{Q}{C} = \frac{1.6 \times 10^{-4}}{32 \times 10^{-6}} = 5 \, \text{V} $.

Question 3

In an isolated system of two capacitors initially charged and then connected in parallel with opposite polarities, what happens to the final energy of the system compared to the initial energy?

Accepted Answer

When two capacitors are connected in parallel with opposite polarities, charges redistribute such that the net charge on the positive plates (and negative plates) adjusts to a new equilibrium. The initial energy stored in the capacitors ($ U_i = \frac{1}{2} C_1 V_1^2 + \frac{1}{2} C_2 V_2^2 $) is greater than the final energy after connection due to energy losses during charge redistribution. Some energy is lost as heat or electromagnetic radiation during the transient current flow, so the final energy is less than the initial energy.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 7

Q2. A \( 16 \, \mu\text{F} \) capacitor charged to \( 10 \, \text{V} \) is connected to an uncharged \( 16 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q3. In an isolated system of two capacitors initially charged and then connected in parallel with opposite polarities, what happens to the final energy of the system compared to the initial energy?

Q4. In a parallel plate capacitor with a partially inserted dielectric slab while maintaining constant charge, why does the capacitance decrease as the slab is withdrawn?

Q5. Why does the potential energy of a dipole in a uniform field increase when rotated from alignment (\( \theta = 0^\circ \)) to perpendicular (\( \theta = 90^\circ \))?

Q6. Three capacitors \( 10 \, \text{pF} \), \( 20 \, \text{pF} \), and \( 40 \, \text{pF} \) are in parallel. What is the total capacitance?

Q7. A spherical conductor of radius 6 cm has a charge of \( 6 \times 10^{-8} \, \text{C} \). 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. Two charges \( 10 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are at \( (8, 0, 0) \) and \( (-8, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q9. A charge of \( 8 \, \mu\text{C} \) is moved from infinity to a point where the potential is \( 50 \, \text{V} \). What is the work done?

Q10. A charged conductor is surrounded by a thin concentric hollow conducting shell. If the shell is grounded, what happens to the charge on the inner conductor?