Question

A wire $X$ of length $50\, cm$ carrying a current of 2 A is placed parallel to a long wire $Y$ of length $5 \, m$. The wire Y carries a current of $3\, A$. The distance between two wires is $5 cm$ and currents flow in the same direction. The force acting on the wire $Y$ is :

• A. $1.2 \times 10^{-5} N$ directed towards wire $X$.
• B. $1.2 \times 10^{-4} N$ directed away from wire $X$.
• C. $1.2 \times 10^{-4} N$ directed towards wire $X$.
• D. $2.4 \times 10^{-5} N$ directed towards wire $X$.

Answer 1

Answer: (A)

Force of interaction $= I _1 \ell_1 B _{12}$
$=\frac{\mu_0 I _1 I _2}{2 \pi r } \ell_1 $
$ =\frac{4 \pi \times 10^{-7} \times 6 \times 0.5}{2 \pi \times 5 \times 10^{-2}} $
$=1.2 \times 10^{-5} \text { towards } X$