Question

A uniform magnetic field of 1.4 T passes through a wire loop of area 0.5 m². If the direction of the field makes a 30° angle with the normal to the plane of the loop. the magnetic flux through the loop is: 
1. 2.8 Wb
2. 6.1 Wb
3. 0.61 Wb
4. 0.30 Wb

Answer 1

Correct Answer - Option 3 : 0.61 Wb

Concept:

Magnetic flux: The number of magnetic field lines passing a surface area normally is called magnetic flux. It is denoted by ϕ.

Magnetic flux is mathematically equal to the dot product of the magnetic field and area vector through which it is passing.

\( {ϕ}=\vec{B}\cdot\vec{A}=BAcos\,θ\)

Where B = magnetic field

A = area vector

θ = angle between B and A

The SI unit of magnetic flux is weber (Wb)

Calculation:

With B = 1.4 T, A = 0.5 m², and θ = 30°, the magnetic flux through the loop will be:

\( {ϕ}=1.4\times 0.5\times cos30^{\circ}\)

\(ϕ = 0.7\times\frac{\sqrt{3}}{{2}}\)

ϕ = 0.60 Wb