Question

An electron moves through a uniform magnetic field $\vec{B} = B_0 \hat{i} + 2B_0 \hat{j} \, \text{T}$. At a particular instant of time, the velocity of the electron is $\vec{u} = 3\hat{i} + 5\hat{j} \, \text{m/s}$. If the magnetic force acting on the electron is $\vec{F} = 5e k \, \text{N}$, where $e$ is the charge of the electron, then the value of $B_0$ is _____ T

Answer 1

The magnetic force is given by:

$\vec{F} = q (\vec{v} \times \vec{B})$

Substituting the values:

$5e \hat{k} = e \left( 3\hat{i} + 5\hat{j} \right) \times \left( B_0 \hat{i} + 2B_0 \hat{j} \right)$

Calculating the cross product:

$5e \hat{k} = e \left( 6B_0 \hat{k} - 5B_0 \hat{k} \right)$

Simplifying:

$5e \hat{k} = e B_0 \hat{k}$

Therefore:

$B_0 = 5T$