Question

Two infinitely long current carrying wires are separeted by $5\text{m}$ lying parallel to each other if current through the first wire is $2.5\text{A}$ upwards then what is the current in the 2nd wire so that magnetic field at the mid point between them is $\frac{{\mu }_0}{4\pi }$ out of the plane of paper-

• A. $\frac{5}{4}\text{A}\text{upward}$
• B. $5\text{A}\text{downwards}$
• C. $2.5\text{A}\text{upward}$
• D. $2.5\text{A}\text{downward}$

Answer 1

The correct option is A $\frac{5}{4}\text{A}\text{upward}$

Let us assume that current in the second wire is upward direction,



If current in the right wire is downward, then we will get the value of current in negative.

Magnetic fields at point $\text{P}$ due to wire-$1$ and wire-$2$ are in opposite direction so,

$B_{net}=B_1-B_2$

$\Rightarrow \frac{{\mu }_0}{4\pi }=\frac{{\mu }_0}{2\pi }\frac{I_1}{a}-\frac{{\mu }_0}{2\pi }\frac{I_2}{a}$

$\Rightarrow \frac{{\mu }_0}{4\pi }=\frac{{\mu }_0}{2\pi }(\frac{2.5}{2.5}-\frac{I_2}{2.5})$

$\frac{1}{2}=1-\frac{I_2}{2.5}$

$\frac{I_2}{2.5}=1-\frac{1}{2}$

$\frac{I_2}{2.5}=\frac{1}{2}$

$\Rightarrow I_2=\frac{2.5}{2}=\frac{5}{4}\text{A}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option (a) is the correct answer.