Question

$A$ and $B$ are two infinitely long straight parallel conductors. $C$ is another straight conductor of length $1m$ kept parallel to A and $B$ as shown in the figure. Then the force experienced by $C$ is

• A. towards $B$ equal to $0.6\times 10^{-5}N$
• B. towards $A$ equal.to $5.4\times 10^{-5}N$
• C. towards $B$ equal to $5.4\times 10^{-5}N$
• D. towards $A$ equal to $0.6\times 10^{-5}$N

Answer 1

Answer: (A)

The force between the conductors is attractive if the currents in them are in the same direction and repulsive if the currents are in opposite direction Mutual force between conductors A and C
$F_1=\frac{{\mu }_0}{2\pi }\frac{I_1{I}_{2}l}{r}$
$=\frac{{\mu }_0}{2\pi }\frac{2\times 3\times 1}{0.05}$
$=2.40\times 10^{-5}N$ (towards A)
Mutual force between conductors B and C
$=\frac{{\mu }_0}{2\pi }\times \frac{4\times 3\times 1}{0.08}$
$=3\times 10^{-5}N$ (towards B)
Hence, the resultant force experienced by C
$=(3-2.4)\times 10^{-5}N$
$=0.6\times 10^{-5}N$ (towards B)