But from the above diagram, I could only infer that the wire breaks. Or in other words, I think there could be no equilibrium as net force is not equal to zero, @JohnRennie sir.
Now suppose the tension in the wire is $T$. As the wire moves inwards its length changes by $dL = 2\pi dr$ i.e. it decreases from $2\pi r$ to $2\pi (r + dr)$.
@JohnRennie: Yes sir. This method is really great and I obtained $F=iBl$ when you were explaining itself (but using some hypothetical assumptions :)). And I got the correct answer. But could you tell whether there is any mistake in the above force diagram? Am I missing any other forces?
@JohnRennie Fine then we shall consider the tension vectors to be nearly vertical but not tangential. If they were exactly tangential, then the net force will be towards the centre and the tension can't counteract the magnetic force, sir.
The forces are indeed not tangential, but metal atoms are very small so if we use a macroscopic radius, i.e. mm or cm, the forces are so nearly tangential that in practice the deviation from the tangential direction is undetectably small.
