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Question

Physics Question on Magnetic Force

Two parallel wires in free space are 10 cm apart and each carries a current of 10 A in the same direction. The force exerted by one wire on the other, per metre length is

A

2×10−4N 2 \times {10} ^{-4} N repulsive

B

2×10−7N 2 \times {10} ^{-7} N repulsive

C

2×10−4N 2 \times {10} ^{-4} N attractive

D

2×10−7N 2 \times {10} ^{-7} N attractive

Answer

2×10−4N 2 \times {10} ^{-4} N attractive

Explanation

Solution

Distance between two parallel wires
(x) = 10 cm = 0.1 m; Current in each wire = I1=I2I_1= I_2
= 10 A and length of wire (l) = 1 m.
Force on the wire (F) = μ0I1⋅I2×l2πx\frac{ {\mu}_0 I_1 \cdot I_2 \times l }{ 2 \pi x }
=(4π×10−7)×10×10×12π×0.1=2×10−4N= \frac{( 4 \pi \times {10}^{-7}) \times 10 \times 10 \times 1}{ 2 \pi \times 0.1 } = 2 \times {10}^{-4} N.
Since the current is flowing in the same direction,
therefore the force will be attractive.