Question

A beam of electrons projected along the $+x$ axis experiences a force due to a magnetic field along the $+y$-axis. What is the direction of the magnetic field?

Answer 1

Step 1: Given Data

The velocity of the electrons $=v\hat{i}$

Force due to the external magnetic field $=F\hat{j}$

The charge of an electron $=-e$

Step 2: Formula Used

We know that the force experienced due to a magnetic field is given as

$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$

where $q$ is the charge of the electrons, $\overrightarrow{v}$ is the velocity of the electrons and $\overrightarrow{B}$ is the external magnetic field.

Step 3: Estimate the Magnetic Field

Upon substituting the values we get,

$F\hat{j}=-ev\hat{i}\times \overrightarrow{B}$

We know that according to the cycle of unit vectors for the cross product we get,

$-\left(\hat{i}\times \hat{k}\right)=\hat{j}$

Therefore, the magnetic field is in the direction of the unit vector $\hat{k}$.

Hence, the direction of the magnetic field is $+z$ axis.