Question

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 \times {10} ^{-4} N$ repulsive
• B. $ 2 \times {10} ^{-7} N$ repulsive
• C. $ 2 \times {10} ^{-4} N$ attractive
• D. $ 2 \times {10} ^{-7} N$ attractive

Answer 1

The Correct Option is C

Distance between two parallel wires
(x) = 10 cm = 0.1 m; Current in each wire = $I_1= I_2 $
= 10 A and length of wire (l) = 1 m.
Force on the wire (F) = $\frac{ {\mu}_0 I_1 \cdot I_2 \times l }{ 2 \pi x }$
$ = \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.