A circular area with a radius of 6.20 cm lies in the x-y plane. A) What is the m

Question

A circular area with a radius of 6.20 cm lies in the x-y plane.

A) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B=0.249 T that points in the +z direction?

B) What is the magnitude of the magnetic flux through the circle due to a uniform magnetic field B=0.249 T that points at an angle of 53.4? from the +z direction?

C) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B= 0.249 T that points in the +y direction?

Explanation / Answer

A.
The xy plane is perpendicular to the z axis meaning the flux is perpendicular to the xy plane. A tesla T is one weber per square meter (w/m^2) so the flux through this circle is 0.249 w/m^2*pi*0.062^2 m^2 = 7.48*10^-4 T = 0.000748 T A. <--------------------

B.
If the angle of the flux were 0 degrees with the z axis, like in the first question, ALL the flux would pass thru the circle. If the angle were 90 degrees with the z axis, NONE would pass thru the circle. So
0.000748* cos53.4 = 0.00074 T

C.
A component of the flux is could be in the Y direction depending upon the choice of which axis is x and which is y. Assume Y is vertical, X is horizontal and Z is out of the page, the Y component would be zero.
If X and Y are swapped, the component would be 0.00074sin53.4

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