Question

A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is

• A. 2 weber
• B. 0.5 weber
• C. 1 weber
• D. Zero weber

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Magnetic flux (\(\Phi\)) is the measure of the total magnetic field that passes through a given area.
It depends on the magnetic field strength, the area of the surface, and the orientation of the surface relative to the field.
Key Formula or Approach:
The magnetic flux \(\Phi\) through a surface area \(A\) in a uniform magnetic field \(B\) is:
\[ \Phi = B A \cos \theta \]
where \(\theta\) is the angle between the magnetic field vector (\(\vec{B}\)) and the area vector (\(\vec{A}\)).
The area vector is always perpendicular to the plane of the surface.
Step 2: Detailed Explanation:
1. Determine the Area (\(A\)):
Side of square loop = 1 m.
Area \(A = \text{side}^2 = 1 \text{ m} \times 1 \text{ m} = 1 \text{ m}^2\).
2. Determine the angle (\(\theta\)):
The problem states the "plane of the loop is perpendicular to the direction of the magnetic field".
This means the magnetic field lines are parallel to the normal (area vector) of the loop.
Therefore, the angle \(\theta = 0^\circ\).
3. Calculate the Flux (\(\Phi\)):
Given \(B = 0.5 \text{ T}\).
\[ \Phi = B \times A \times \cos 0^\circ \]
\[ \Phi = 0.5 \times 1 \times 1 \]
\[ \Phi = 0.5 \text{ Weber} \]
Note: The resistance of the loop is given but is not required to calculate the magnetic flux.
Step 3: Final Answer:
The magnetic flux through the loop is 0.5 weber.