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.

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.