NEET Electrostatic Potential and Capacitance — Set 16

Question 1

A charge of $ 3 \, \mu\text{C} $ is brought from infinity to a point where the potential is $ 400 \, \text{V} $. What is the work done?

Accepted Answer

Work done = Potential energy = $ q V $. $ W = 3 \times 10^{-6} \times 400 = 1.2 \times 10^{-3} \, \text{J} = 1.2 \, \text{mJ} $.

Question 2

Three charges $ +3 \, \mu\text{C} $, $ -2 \, \mu\text{C} $, and $ +4 \, \mu\text{C} $ are at $ (0, 0, 0) $, $ (3, 0, 0) $, and $ (0, 4, 0) \, \text{m} $. What is the potential at $ (3, 4, 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{(3-0)^2 + (4-0)^2} = 5 \, \text{m} $, $ r_2 = 4 \, \text{m} $, $ r_3 = 3 \, \text{m} $. $ V = 9 \times 10^9 \left( \frac{3 \times 10^{-6}}{5} + \frac{-2 \times 10^{-6}}{4} + \frac{4 \times 10^{-6}}{3} \right) $. $ V = 9 \times 10^9 \left( 0.6 \times 10^{-6} - 0.5 \times 10^{-6} + 1.33 \times 10^{-6} \right) = 9 \times 10^9 \times 1.43 \times 10^{-6} = 1.287 \times 10^4 \, \text{V} \approx 12870 \, \text{V} $.

Question 3

A $ 3 \, \mu\text{F} $ capacitor is charged to $ 300 \, \text{V} $. What is the energy stored in it?

Accepted Answer

$ U = \frac{1}{2} C V^2 = \frac{1}{2} \times 3 \times 10^{-6} \times (300)^2 = \frac{1}{2} \times 3 \times 10^{-6} \times 9 \times 10^4 = 0.135 \, \text{J} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 16

Q1. A charge of \( 3 \, \mu\text{C} \) is brought from infinity to a point where the potential is \( 400 \, \text{V} \). What is the work done?

Q3. A \( 3 \, \mu\text{F} \) capacitor is charged to \( 300 \, \text{V} \). What is the energy stored in it?

Q4. A charge of \( 6 \, \mu\text{C} \) is moved from infinity to a point where the potential is \( 150 \, \text{V} \). What is the work done?

Q5. A parallel plate capacitor with \( C = 40 \, \text{pF} \) in air has a dielectric (\( K = 5 \)) inserted fully between plates. What is the new capacitance?

Q7. A charge of \( 5 \, \mu\text{C} \) is moved from infinity to a point where the potential is \( 300 \, \text{V} \). What is the work done?

Q8. A conductor has a surface charge density of \( 5.5 \times 10^{-6} \, \text{C/m}^2 \). What is the electric field just outside it? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q9. A point charge \( Q = 15 \times 10^{-9} \, \text{C} \) is placed at the origin. Calculate the potential at a point 5 m away from the charge. (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q10. A dipole \( p = 7 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 90^\circ \) to \( 0^\circ \) in a field \( E = 2 \times 10^5 \, \text{N/C} \). What is the work done?