A circular area with a radius of 6.10 cm lies in the x y -plane. Part A What is

Question

A circular area with a radius of 6.10 cm lies in the xy-plane.

Part A

What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field with a magnitude of 0.220 T in the + z -direction?

______

Part B

What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magnitude of 0.220 T ), now at an angle of 51.7 from the   + z -direction?

_______

Part C

What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magntiude of 0.220 T ), now in the + y -direction?

_______

Explanation / Answer

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 0.22 w/m^2*pi*0.061^2 m^2 = 0.00257w/m^2

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
0.00257* cos51.7 = 0.001592 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.

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