A circular area with a radius of 6.50 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.230 T (a) in the +z-direction; (b) at an angle of 53.1∘ from the +z-direction; (c) in the +y-direction?

Explanation:

#Consider a circular area of radius in the xy-plane at z=0. This means all the are vector points toward the +ve z-axis.

a. first, find the magnetic flux if the magnetic field has a magnitude of and points toward the +ve z-axis. The angle between the magnetic field and the area is . Hence the magnetic flux:-

Hence flux magnitude in direction is

b. We now find the magnetic flux when the field has a magnitude of B=0.230T and points at an angle of from the direction.

Magnetic flux is calculated as:

Hence the flux at an angle of is

c. We now need to find the magnetic flux if the field has a magnitue of B=0.230T and points in the direction of +y-direction. As with the previous parts, the magnetic flux will be calculated as:

Hence the magnetic flux in the +y-direction is zero.