A. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field with a magnitude of 0.300 T in the + z direction?
B. What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magnitude of 0.300 T), now at an angle of 54.1^circ from the + z direction?
C. is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magntiude of 0.300 T), now in the + y direction?
3 Answers

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 0.3 w/m^2pi0.063^2 m^2 = 3.74e3 w/m^2 = 3.74*10^3 T = 0.00374 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
0.00374* cos54.1 = 0.0022 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 0.0022sin54.1

Oldschool is correct in A and B, except in C the angle would be 90 degrees which would make the flux be zero

i’m no longer tremendous at maths yet i imagine it quite works because: a million) Pi is the perspective of the arc (the consistent veer of the circle) 2) the radius is 1/2 of the diameter, so in case you’ve been to spin that infant 360 ranges, you would possibly want to get the realm (assuming you extremely a lot recognize a thanks to get the realm of a sq. of another second structure) so in reality A= Pi x r * (the position * is the sq. funtion) is type of like expressing the realm clone of a rectangle as an social gathering, yet you’re limting it to the arc of the circle