NEET Electrostatic Potential and Capacitance — Set 18

Question 1

A conductor has a surface charge density of $ 4.5 \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} $).

Accepted Answer

$ E = \frac{\sigma}{\varepsilon_0} = \frac{4.5 \times 10^{-6}}{8.85 \times 10^{-12}} \approx 5.085 \times 10^5 \, \text{N/C} $.

Question 2

A charge of $ 2 \, \mu\text{C} $ is moved from infinity to a point with potential $ 500 \, \text{V} $. What is the work done?

Accepted Answer

Work done = Potential energy = $ q V $. $ W = 2 \times 10^{-6} \times 500 = 10^{-3} \, \text{J} = 1 \, \text{mJ} $.

Question 3

A conductor has a surface charge density of $ 1.5 \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} $).

Accepted Answer

$ E = \frac{\sigma}{\varepsilon_0} = \frac{1.5 \times 10^{-6}}{8.85 \times 10^{-12}} \approx 1.695 \times 10^5 \, \text{N/C} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 18

Q1. A conductor has a surface charge density of \( 4.5 \times 10^{-6} \, \text{C/m}^2 \). What is the electric field just outside it? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q2. A charge of \( 2 \, \mu\text{C} \) is moved from infinity to a point with potential \( 500 \, \text{V} \). What is the work done?

Q3. A conductor has a surface charge density of \( 1.5 \times 10^{-6} \, \text{C/m}^2 \). What is the electric field just outside it? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q4. When a charged conductor is placed in contact with an uncharged conductor of smaller size, why does the smaller conductor acquire a higher surface charge density upon reaching equilibrium?

Q5. In a system where a positively charged sphere is enclosed by an uncharged conducting shell, why does the outer surface of the shell acquire a negative charge if a negative charge is brought near it?

Q6. Two charges \( 14 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) are at \( (3, 0, 0) \) and \( (-3, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q7. A parallel plate capacitor has plates of area \( 0.05 \, \text{m}^2 \) and separation 0.25 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q8. A \( 3 \, \mu\text{F} \) capacitor charged to \( 200 \, \text{V} \) is connected to an uncharged \( 9 \, \mu\text{F} \) capacitor. What is the energy lost?

Q9. Two capacitors of \( 30 \, \text{pF} \) and \( 60 \, \text{pF} \) are connected in series. What is the equivalent capacitance?

Q10. An electric dipole with moment \( p = 2 \times 10^{-10} \, \text{C m} \) is at the origin, aligned along the x-axis. What is the potential at \( (0, 2, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).