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Actually I had posted a very similar question, but I wasn't quite satisfied with the answer so I am posting a new variety again.

Imagine an infinitely long wire carrying current $I_1$ from West to East. At a small distance $d$ above the wire there is another small current carrying wire of length $l$ carrying current $I_2$ from East to West (opposite to the direction of current in the below placed wire). Obviously they are magnetically repelling. And if the second wire (carrying current from East to West) is at rest the magnetic force must be equal to $mg$.

The magnetic force is upward and $mg$ is down. The magnetic force can be written as $$\frac{Uo I_1I_2}{2\pi d} l = mg$$ Now, if the magnetic force is greater than $mg$, the wire moves up. Now magnetic force is up and displacement is up too which means that work done by magnetic force should be positive. How is that possible when we know that work done by a magnetic force is always zero? Is it that an e.m.f. is induced which opposes the change?

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Mohammad Abid
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2 Answers2

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Here is the misunderstanding:

Now, if the magnetic force is greater than mg, the wire moves up. Now magnetic force is up and displacement is up too which means that work done by magnetic force should be positive.

The statement that a magnetic field does no work is of a static magnetic field. You are positing a changing magnetic field by the word "greater" and "moves". To become greater energy has been supplied and it is not the static condition. That changing magnetic fields do work is evident :

An electromagnetic crane is a type of crane with an electromagnetic lift. Electromagnetic cranes are commonly utilized in lifting and moving various scrap metals. It does not have the mechanical 'pincers' of a regular crane, instead, it has a large flat magnet which draws the metallic materials to it.

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anna v
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Im somehow not able to comment on anna v answer so here goes my cmment

How isnt the magnetic field non static. Acc. To The relation the force is dependent on the the magnitudes of current. Lets suppose some constant current i1 is flowing in the below placed wire and we bring the wire 2 also carrying some dc constant current i2 and place it above the i1 wire. The moment we place the wire 2 in the field of 1 the repelling force is experienced by the wire 2. And for instance the magnetic force which is constant as i1 and i2 are constants exceeds the mg downwards the wire 2 moves up, the work is certainly done by static magnetic field. I dont see any other parameter which could change the magnitude of magnetic field and make it varying.

Mohammad Abid
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