Question

A long straight wire carrying a current of $30A$ is placed in an external uniform magnetic field of induction $4\times {10}^{-4}T$. The magnetic field is acting parallel to the direction of the current. The magnitude of the resultant magnetic induction in tesla at a point $2.0cm$ away from the wire is :
$[{\mu }_0=4\pi \times {10}^{-7}H{m}^{-1}]$

• A. ${10}^{-4}$
• B. $3\times {10}^{-4}$
• C. $5\times {10}^{-4}$
• D. $6\times {10}^{-4}$

Answer 1

The correct option is C $5\times {10}^{-4}$

Magnetic field due to the wire is perpendicular to the applied field.
$B_1=\frac{{\mu }_{0}i}{2\pi r}=\frac{2\times {10}^{-7}\times 30}{2\times {10}^{-2}}=3\times {10}^{-4}T$
$\therefore$ resultant magnetic Induction $B=\sqrt{{B_1}^2+{B_1}^2}=B=\sqrt{\left(3^2\right)+{\left(4\right)}^2}\times {10}^{-4}=5\times {10}^{-4}T$