Physics - Magnetism Question with Solution | TestHub

The magnetic field produced by a long solenoid along its axis is given by $B={\mu }_{0}nI$, where $n$ is the number of turns per unit length and $I$ is the current.

Given that the new number of turns per unit length is $n^{\prime }=3n$ and the new current is $I^{\prime }=\frac{I}{4}$.

The new magnetic field $B^{\prime }$ is given by:

$B^{\prime }={\mu }_0{n}^{\prime }{I}^{\prime }$

$B^{\prime }={\mu }_0(3n)\left(\frac{I}{4}\right)$

$B^{\prime }=\frac{3}{4}{\mu }_{0}nI$

$B^{\prime }=\frac{3B}{4}$

Answer: $\frac{3B}{4}$