Question

A wire of length l carries a current i long the x-axis. A magnetic field exists, which is given as →B=B0(→i+→j+→k) T. Find the magnitude of the magnetic force acting on the wire.

Answer 1

To Find: The magnitude of the magnetic force acting on the wire.

Explanation:

Given:

A wire of length l cm

Electric current through the wire is i.

$\text { Magnetic field, } \vec{B}=B_{0}(\vec{i}+\vec{j}+\vec{k}) T$

As per the question, the current is passing along X axis.

Magnetic Field,

$\vec{F}=\vec{i} l \times \vec{B}$

Putting the respective values in the above equation, we get:

$=i\left\{(\overrightarrow{l i}) \times\left(B_{0} \vec{i}+B_{0} \vec{j}+B_{0} \vec{k}\right)\right\}$

$=i\left\{I B_{0} \vec{k}-I B_{0} \vec{j}\right\}$

The magnitude of the magnetic force,

$|\vec{F}|=\sqrt{2 i^{2} l^{2} B_{0}^{2}}$