I am really struggling with this problem about flux through a flat surface of fixed length in xy-plane. Help?

Hi guys and gals, I don't know what to do about this flux problem b/c I haven't got there in vector calc, and my instructor wasn't too clear on it and we discussed it a while ago with Gaussian surfaces. The problem is:

A flat square surface of side length 3.90 lies in the xy-plane at z=0. Find the flux through this surface produced by a magnetic field B(vector)=(0.200T)i+(0.300T)j-(0.450T)k. Express your answer in appropriate units.

I'd appreciate a rundown of how to go through this and I will definitely give 10 pts to the first/most complete answer. Thank you very much for the time.

2 Answers

  • The surface is S= 3.90*3.90 =15.21 k , because XY plane has a normal direction of k , so

    Flux= F .dS = )=(0.200T)i+(0.300T)j-(0.450T)k . 15.21 k

    = -0.45 T *15.21 = -6.8445 (Weber ) or (Wb)

  • magnetic flux = Integral {B dot dA)

    But you won't have to do this for the problem you posted because of the symmetry in the problem. Since the surface lies on the xy plane, only the z- component of the magnetic field should you use. In short, the answer is the area of the surface times the z-component of the magnetic field. Don't forget to change the units into the right system of units.

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