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Question

A long horizontally fixed wire carries a current of $$100$$ ampere. Directly above and parallel to it is a fine wire that carries a current of $$20$$ ampere and weights $$0.04$$ newton per meter. The distance between the two wires for which the upper wire is just supported by magnetic repulsion is:


A
102mm
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B
102cm
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C
102m
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D
102km
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Solution

The correct option is C $$10^{-2}m$$
Force on the wire element per unit length is given by:
$$F = \cfrac{\mu_o I_1 I_2}{ 2 \pi r}$$
This balances the weight of the wire per unit length
$$0.04 = \cfrac{2 \times 10^{-7} \times 100 \times 20}{r}$$
$$r = 10^{-2}\ m$$

Physics

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