NEET Electrostatic Potential and Capacitance — Set 6

Question 1

A parallel plate capacitor with capacitance $ 100 \, \text{pF} $ has a dielectric ($ K = 3 $, thickness $ d/3 $) inserted. What is the new capacitance? (Original separation $ d $).

Accepted Answer

Potential difference: $ V = E_0 \left( \frac{2d}{3} \right) + \frac{E_0}{K} \left( \frac{d}{3} \right) = E_0 d \left( \frac{2}{3} + \frac{1}{3 \times 3} \right) $. $ V = E_0 d \left( \frac{2}{3} + \frac{1}{9} \right) = E_0 d \times \frac{7}{9} $. $ C = \frac{Q}{V} = \frac{Q}{\frac{7}{9} V_0} = \frac{9}{7} \times 100 \approx 128.57 \, \text{pF} $.

Question 2

Three charges $ +6 \, \mu\text{C} $, $ -3 \, \mu\text{C} $, and $ +1 \, \mu\text{C} $ are at $ (0, 0, 0) $, $ (6, 0, 0) $, and $ (0, 6, 0) \, \text{m} $. What is the potential at $ (6, 6, 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{6^2 + 6^2} = 6\sqrt{2} \, \text{m} $, $ r_2 = 6 \, \text{m} $, $ r_3 = 6 \, \text{m} $. $ V = 9 \times 10^9 \left( \frac{6 \times 10^{-6}}{6\sqrt{2}} + \frac{-3 \times 10^{-6}}{6} + \frac{1 \times 10^{-6}}{6} \right) $. $ V = 9 \times 10^9 \left( \frac{6 \times 10^{-6}}{8.485} - \frac{3 \times 10^{-6}}{6} + \frac{1 \times 10^{-6}}{6} \right) $. $ V = 9 \times 10^9 \left( 0.707 \times 10^{-6} - 0.5 \times 10^{-6} + 0.167 \times 10^{-6} \right) $. $ V = 9 \times 10^9 \times 0.374 \times 10^{-6} = 3366 \, \text{V} $.

Question 3

Two charges $ 24 \, \mu\text{C} $ and $ -12 \, \mu\text{C} $ are placed 24 cm apart. What is the potential energy of the system? (Take $ \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} $).

Accepted Answer

$ U = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r} = 9 \times 10^9 \times \frac{24 \times 10^{-6} \times (-12 \times 10^{-6})}{0.24} $. $ U = 9 \times 10^9 \times \frac{-288 \times 10^{-12}}{0.24} = -10.8 \, \text{J} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 6

Q1. A parallel plate capacitor with capacitance \( 100 \, \text{pF} \) has a dielectric (\( K = 3 \), thickness \( d/3 \)) inserted. What is the new capacitance? (Original separation \( d \)).

Q3. Two charges \( 24 \, \mu\text{C} \) and \( -12 \, \mu\text{C} \) are placed 24 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q4. A \( 12 \, \mu\text{F} \) capacitor charged to \( 30 \, \text{V} \) is connected to an uncharged \( 12 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q5. A conductor has a surface charge density of \( 5 \times 10^{-7} \, \text{C/m}^2 \). What is the electric field just outside it? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q6. What is the work done in moving a \( 5 \, \mu\text{C} \) charge from infinity to a point where the potential is \( 2000 \, \text{V} \)?

Q7. A conductor has a surface charge density of \( 2.5 \times 10^{-6} \, \text{C/m}^2 \). What is the electric field just outside it? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q8. A conductor has a surface charge density of \( 3 \times 10^{-6} \, \text{C/m}^2 \). What is the electric field just outside it? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q9. An electric dipole with moment \( p = 4 \times 10^{-9} \, \text{C m} \) lies along the x-axis. What is the potential at \( (-2, 0, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q10. In a system of two parallel plate capacitors with different dielectrics connected in parallel, why does the capacitor with a higher dielectric constant store more energy for the same applied voltage?