Question

Two infinitely long, thin, insulated, straight wires lie in the $x-y$ plane along $x$ and $y–\text{axes}$, respectively. Each wire carries a current $I$, respectively, in the positive $x–$ direction and positive $y–$ direction. The magnetic field will be zero at all points on the straight line.

• A. $y=x-1$
• B. $y=-x$
• C. $y=-x+1$
• D. $y=x$

Answer 1

The correct option is D $y=x$

$\to$ At a point $P$ on the line $y=x$, the Magnetic field due to wire $\left(1\right)$ will be upwards in the first quadrant and is downwards in the third quadrant.

$\to$ At a point $P$ on the line $y=x$, the Magnetic field due to wire $\left(2\right)$ will be downwards in the first quadrant and is upwards in the third quadrant.

$\to$ So, along the line $y=x$ , the above two values of magnetic field are equal and opposite in direction and hence their resultant is zero.

Hence, option (A) is correct.