Question

A circular area with a radius of 5.70 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.185 T oriented in the following ways?

(a) in the +z-direction
_________ Wb

(b) at an angle of 53.1

Answer 1

Remember that:

$\Phi = \vec{B}\cdot \vec{A} = B(\pi r^2) \cos\theta$

a) if B is in the z+ direction the angle is zero so:

$\Phi = B(\pi r^2) = 0.185(\pi(0.057)^2)= 1.883 \times 10^{-3} Wb$

b) if B is at angle of 53.1 from the +z direction:

$\Phi = B(\pi r^2) \cos\(53.1) = (0.185)(\pi(0.057)^2)\cos(53.1) = 1.1338 \times 10^{-3} Wb$

c) if B is in the y direction the angle is 90:

$\Phi = B(\pi r^2) \cos\(90) = 0 Wb$