NEET Electric Charges and Fields — Set 17

Question 1

A conducting sphere of radius 20 cm has an electric field of $ 3 \times 10^3 \, \text{N/C} $ at 40 cm from its center. What is its charge?

Accepted Answer

For a conductor, $ E = \frac{k q}{r^2} $ outside. $ 3 \times 10^3 = 9 \times 10^9 \times \frac{q}{(0.4)^2} $. $ q = \frac{3 \times 10^3 \times 0.16}{9 \times 10^9} = 5.33 \times 10^{-8} \, \text{C} $.

Question 2

A uniform electric field $ E = 7 \times 10^3 \, \text{N/C} $ is along the x-axis. What is the flux through a rectangle of 25 cm × 40 cm in the yz-plane?

Accepted Answer

Area vector $ \Delta \mathbf{S} = 0.25 \times 0.4 = 0.1 \, \text{m}^2 $ along x-axis. Flux: $ \phi = \mathbf{E} \cdot \Delta \mathbf{S} = 7 \times 10^3 \times 0.1 = 700 \, \text{Nm}^2/\text{C} $.

Question 3

What characteristic of conductors allows charges to distribute uniformly over their surface when placed in an external electric field?

Accepted Answer

In conductors, charges (free electrons) can move freely. In an external field, they redistribute until the internal field cancels the external field, achieving equilibrium. This results in charges residing only on the surface, distributed uniformly for a spherical conductor due to symmetry.

NEET Physics: Electric Charges and Fields — Practice Set 17

Q1. A conducting sphere of radius 20 cm has an electric field of \( 3 \times 10^3 \, \text{N/C} \) at 40 cm from its center. What is its charge?

Q2. A uniform electric field \( E = 7 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a rectangle of 25 cm × 40 cm in the yz-plane?

Q3. What characteristic of conductors allows charges to distribute uniformly over their surface when placed in an external electric field?

Q4. Why does the electric field due to a dipole have both radial and tangential components at a general point?

Q5. An infinite line charge has \( E = 3.6 \times 10^5 \, \text{N/C} \) at 10 cm. What is \( \lambda \)?

Q6. A spherical shell has a net flux of \( 1.13 \times 10^5 \, \text{Nm}^2/\text{C} \) through it. What is the charge enclosed?

Q7. A point charge \( q = 5 \, \mu\text{C} \) is placed at the origin. What is the electric field magnitude at a point 2 m away along the x-axis?

Q8. A thin spherical shell of radius 18 cm has \( q = 12 \, \mu\text{C} \). What is the electric field at 22 cm from the center?

Q9. A plastic rod gains a charge of \( -1.28 \times 10^{-7} \, \text{C} \) when rubbed. How many electrons were transferred to it?

Q10. An infinite line charge has \( E = 6.0 \times 10^5 \, \text{N/C} \) at 3 cm. What is \( \lambda \)?