Question

A particle of charge q and mass m starts moving from the origin under the action of an electric field $\overrightarrow{E}=E_0\hat{i}$ and magnetic field $\overrightarrow{B}=B_0\hat{k}$. Its velocity at (x,0,0) is $(6\hat{i}+8\hat{j})$. The value of x is

• A. $\frac{25m}{q{E}_0}$
• B. $\frac{100m}{q{E}_0}$
• C. $\frac{50m}{q{E}_0}$
• D. $\frac{14m}{q{E}_0}$

Answer 1

The correct option is C $\frac{50m}{q{E}_0}$

Speed of the particle at $(x_{0}0,0)$ is $10$ units.

Applying work energy theorem and realising the fact that the

magnetic force do no work give the value of$x_0$.

$\begin{array}{c}q{E}_0{x}_0=\frac{1}{2}m{v}^2\\ =\frac{1}{2}\times m\times 10\times 10\\ =50m\\ then,\\ =\frac{50m}{q{E}_0}\end{array}$

Hence,

Option $C$ is correct answer.