Question

A rectangular loop of size 5 cm × 8 cm is lying in x-y plane in a uniform magnetic field \(\vec{B} = (2.0 \text{ T}) \hat{k}\). The total magnetic flux linked with the loop is:

• A. 80 Wb
• B. 16 Wb
• C. \(8 \times 10^{-2}\) Wb
• D. \(8 \times 10^{-3}\) Wb

Hint:

Always convert cm² to m² by multiplying by \(10^{-4}\). It is a very common point where students lose marks!

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Magnetic flux (\(\Phi\)) is the measure of the total magnetic field passing through a given area. When the area is perpendicular to the field, the flux is simply the product of the field magnitude and the area.

Step 2: Key Formula or Approach:
\(\Phi = \vec{B} \cdot \vec{A} = BA \cos \theta\).

Step 3: Detailed Explanation:
1. Area \(A = 5 \text{ cm} \times 8 \text{ cm} = 40 \text{ cm}^2 = 40 \times 10^{-4} \text{ m}^2 = 4 \times 10^{-3} \text{ m}^2\). 2. The loop is in the x-y plane, so its area vector points in the z-direction (\(\hat{k}\)). 3. The magnetic field is \(\vec{B} = 2.0 \hat{k}\). 4. Since \(\vec{B}\) and \(\vec{A}\) are parallel, \(\theta = 0^\circ\) and \(\cos \theta = 1\). \[ \Phi = B \times A = 2.0 \times (4 \times 10^{-3}) = 8 \times 10^{-3} \text{ Wb} \]

Step 4: Final Answer:
The total magnetic flux is \(8 \times 10^{-3}\) Wb.