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

Correct Answer: 5

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:

\[ B_0 = 5T \]