Question

A long straight wire carrying a current of $30 \, A$ is placed in an external uniform magnetic field of induction $4\times 10^{- 4} \, T$ . The direction of external magnetic field is along the direction of the current. The magnitude of the resultant magnetic induction at a point $2.0 \, cm$ away from the wire is $n\times 10^{- 4}T$ . What is the value of $n$ ?

Answer 1

Magnetic field due to wire
$B=\frac{\mu _{0} I}{2 \pi r}=\frac{4 \pi \times 1 0^{- 7}}{2 \pi }\times \frac{30}{2 \times 1 0^{- 2}}$
$=3\times 10^{- 4} \, T$
This magnetic field will be perpendicular to external magnetic field.
$\therefore $ Net magnetic field
$B =\sqrt{ B ^{2}+ B _{0}^{2}}$
$=\sqrt{\left(3 \times 10^{-4}\right)^{2}+\left(4 \times 10^{-4}\right)^{2}}$
$=5\times 10^{- 4} \, T$