Question

Two parallel wires carrying the currents $I$ and $2I$ in the same direction have magnetic field $B$ at the midpoint between them. If the current $2I$ is switched off, the magnitude of magnetic field at that point will be :

• A. $0.5B$
• B. $B$
• C. $2B$
• D. $3B$

Answer 1

The correct option is B $B$

Magnetic field at Mid-point when $2I$ is on.
$=\frac{{\mu }_{0}2I}{2\pi r}+\frac{{\mu }_0(-I)}{2\pi r}$
$=\frac{{\mu }_{0}I}{2\pi r}=B$
Magnetic field at Mid-point when $2I$ is switched off.
$=\frac{{\mu }_0\left(0\right)I}{2\pi r}+\frac{{\mu }_0(-I)}{2\pi r}$
$=-\frac{{\mu }_{0}I}{2\pi r}=-B$
So, magnitude will be $B$ but in opposite direction