Physics - Magnetism Question with Solution | TestHub

Velocity of the proton, $\vec{v}=v\hat{i}$

Magnetic field, $\vec{B}=B_0\hat{k}$

For the proton to move at a constant velocity, the net force acting on it must be zero.

Lorentz force, $\vec{F}=q(\vec{E}+\vec{v}\times \vec{B})=0$

$\vec{E}=-(\vec{v}\times \vec{B})$

$\vec{E}=-(v\hat{i}\times B_0\hat{k})$

$\vec{E}=-v{B}_0(\hat{i}\times \hat{k})$

Since $\hat{i}\times \hat{k}=-\hat{j}$

$\vec{E}=-v{B}_0(-\hat{j})=v{B}_0\hat{j}$

Answer: $v{B}_0\hat{j}$