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 unit length] is

• A. $2 \times 10^{-4} Nm ^{-1}$ [attractive]
• B. $2 \times 10^{-7} Nm ^{-1}$ [attractive]
• C. $2 \times 10^{-4} Nm ^{-1}$ [repulsive]
• D. $2 \times 10^{-7} Nm ^{-1}$ [repulsive]

Answer 1

Answer: (A)

$\frac{ F }{l} =\left(\frac{\mu_{0}}{4 \pi}\right) \frac{2 I _{1} I _{2}}{ d } $
$=\frac{10^{-7} \times 2 \times 10 \times 10}{10 \times 10^{-2}}$
$\frac{ F }{l}=2 \times 10^{-4} N m ^{-1}$
[attractive since the currents are in the same direction]