The magnetic field between the poles of a magnet has magnitude 0.510 T. A circular loop of wire with radius 3.20 cm is placed between the poles so the field makes an angle of 22.0° with the plane of the loop. What is the magnetic flux through the loop?

The magnetic flux through the loop is 0.00478 T. m²

Explanation:

Given;

magnitude of magnetic field, B = 0.510 T

radius of the circular loop, r = 3.2cm

angle between the fields, θ = 22.0°

Area of the loop:

A = πr²

A = π (0.032) ² = 0.0101 m²

Φ = BAcosθ

where;

Φ is the the magnetic flux through the loop

Φ = BAcosθ

Φ = 0.51 x 0.0101 x cos22°

Φ = 0.005151 x 0.9272

Φ = 0.00478 T. m²

Therefore, the magnetic flux through the loop is 0.00478 T. m²

1.52*10⁻³ Wb

Explanation:

Using

Φ = BAcosθ ... Equation

Where, Φ = magnetic Field, B = 0.510 T, A = cross sectional area of the loop, θ = angle between field and the plane of the loop

Given: B = 0.510 T, θ = 22°,

A = πr², Where r = radius of the circular loop = 3.20 cm = 0.032 m

A = 3.14 (0.032²)

A = 3.215*10⁻³ m²

Substitute into equation 1

Ф = 0.510 (3.215*10⁻³) cos22°

Ф = 0.510 (3.215*10⁻³) (0.927)

Ф = 1.52*10⁻³ Wb

Hence the magnetic flux through the loop = 1.52*10⁻³ Wb