Question

A rectangular coil of size 15 cm \( \times \) 20 cm is placed in XY plane in a region of uniform electric field \( 3 \times 10^3 \, {KVm}^{-1} \). Then the electric flux through the coil is:

• A. 9 Vm
• B. 90 Vm
• C. 900 Vm
• D. 99 Vm

Hint:

Electric flux is calculated by multiplying the electric field with the area and the cosine of the angle between them.

Answer 1

The Correct Option is B

We are given the size of the coil, which is 15 cm \( \times \) 20 cm. Converting to meters, the dimensions become 0.15 m \( \times \) 0.20 m. 
The area \( A \) of the coil is given by: \[ A = {length} \times {width} = 0.15 \times 0.20 = 0.03 \, {m}^2 \] The electric field \( E \) is \( 3 \times 10^3 \, {KVm}^{-1} \) or \( 3 \times 10^6 \, {Vm}^{-1} \). Now, electric flux \( \Phi_E \) is given by: \[ \Phi_E = E \cdot A \] Since the electric field is parallel to the coil, the angle between the electric field and the normal to the surface is 0 degrees, so: \[ \Phi_E = 3 \times 10^6 \times 0.03 = 90 \, {Vm} \] Final Answer: 90 Vm