Question

A coil having 100 turns and area $0.02\ \text{m}^{2}$ is placed perpendicular to a magnetic field of $1\ \text{Wb m}^{-2}$. The magnetic flux linked with the coil is:

• A. zero
• B. 1 Wb
• C. 2 Wb
• D. 3 Wb
• E. 5 Wb

Hint:

"Perpendicular to the field" means $\theta = 0^\circ$ for the area vector.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem asks for the total magnetic flux linked with a coil in a uniform magnetic field. Magnetic flux is a measure of the total magnetic field lines passing through a given area.
Step 2: Key Formula or Approach:
1. Magnetic Flux (\( \Phi_B \)) through a single loop is given by: \[ \Phi_B = B A \cos\theta \] where B is the magnitude of the magnetic field, A is the area of the loop, and \( \theta \) is the angle between the magnetic field lines and the normal (perpendicular) to the plane of the loop. 2. Total Flux Linked with a Coil: For a coil with N turns, the total flux linkage is the flux through one turn multiplied by the number of turns. \[ \Phi_{total} = N \Phi_B = N B A \cos\theta \] Step 3: Detailed Explanation:
We are given: - Number of turns, N = 100 - Area of the coil, A = 0.02 m\(^2\) - Magnetic field strength, B = 1 Wb/m\(^2\) (or 1 Tesla) The problem states that the plane of the coil is perpendicular to the magnetic field. This means the magnetic field lines are passing straight through the coil. The angle \( \theta \) in the formula is the angle between the magnetic field vector and the normal to the plane of the coil. If the plane is perpendicular to the field, its normal vector is parallel to the field. Therefore, the angle \( \theta = 0^\circ \). And \( \cos(0^\circ) = 1 \). Now, calculate the total magnetic flux: \[ \Phi_{total} = N B A \cos\theta \] \[ \Phi_{total} = 100 \times 1 \times 0.02 \times \cos(0^\circ) \] \[ \Phi_{total} = 100 \times 1 \times 0.02 \times 1 \] \[ \Phi_{total} = 2 \text{ Wb} \] Step 4: Final Answer:
The magnetic flux linked with the coil is 2 Wb.