A rectangular loop of wire with width 0.4 cm and length 0.4 cm is oriented with the normal to the face of the loop making an angle of 30° with respect to the direction of B. The B field has a magnitude of 0.77 T. Find the magnetic flux through the loop.

0.001067 Wb

Explanation:

Parameters given:

Magnetic field, B = 0.77 T

Angle, θ = 30º

Width = 0.4cm = 0.04m

Length = 0.4cm = 0.04m

Magnetic flux, Φ(B) is given as:

Φ(B) = B * A * cosθ

Where A is Area

Area = length * width = 0.04 * 0.04 = 0.0016 m²

Φ(B) = 0.77 * 0.0016 * cos30

Φ(B) = 0.00167 Wb

1.07×10⁻⁵ Wb

Explanation:

Using

Φ = BAcosθ Equation 1

Where Φ = magnetic Flux, B = magnetic Field, A = Area of the rectangular loop, Angle between the loop and the Field.

But

A = L×W Equation 2

Where L = Length, W = Width.

Substitute equation 2 into equation 1

Φ = BLWcosΦ Equation 3

Given: B = 0.77 T, L = 0.4 cm = 0.004 m, W = 0.4 cm = 0.004 m, Ф = 30°

Substitute into equation 3

Ф = 0.77(0.004)(0.004)cos30

Ф  = 1.07×10⁻⁵ Wb.

Hence the magnetic Field through the loop = 1.07×10⁻⁵ Wb.