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I have a task to solve in electrodynamics, I have really no clue how to solve. Would be very thankful if someone could help!

There is a live conductor loop L, which is situated in a magnetic field B.

Force of the conductor loop:

enter image description here

Magnetic field is homogeneous and shows in z-direction, B = B*e_z

Now I want to show that x-component of force is given as

enter image description here

and show value of F_y and F_z. How could force be calculated with Stokes´formula ?

Tanks in advance!

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A bad misconception! In homogenic magnetic field you can move the whole cross product and the field density vector outside the integral, you integrate only the differential of the position vector. That's zero around a closed loop, there's no cumulated force to your current loop. Parts of the loop surely get some force and there can well be a torque, as we have in electric motors.

I guess your actual task will remain unsolved, if you build on the assumption that a closed current loop catches a non-zero resultant force in a homogenic magnetic field. Maybe you should reveal the task. If the math problem that you presented is the exact task you have got, it's a prank.

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  • \$\begingroup\$ Hey, thanx for your comment. Unfortunately the task is exactly like posted :) \$\endgroup\$ – Tom May 28 at 11:41

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