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What they tell total force for the circuit with current will be zero in the permanent homogeneous magnetic field. I understand, that circuit always should be closed (in a kind of loop) and on the one side of the circuit will be one force, on another side force will be in a different direction which gives zero in total.

But what if half of the circuit we will cover by magnetic shield like described here?

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If you place a "mu-metal" shield around part of the circuit, then the magnetic field won't be homogeneous in that region, and the net force will not necessarily be zero.

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