Question

A particle of mass m and charge q 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 $(x_0,0,0)$ is $(4\hat{i}+3\hat{j})$. Then

• A. $x_0=\frac{25m}{2q{E}_0}$
• B. $x_0=\frac{5q}{2B_{0}m}$
• C. $x_0=\frac{16q{E}_0}{m{B}_0}$
• D. $x_0=\frac{13q{E}_0}{2m{B}_0}$

Answer 1

The correct option is A

$x_0=\frac{25m}{2q{E}_0}$

Let q be the charge and m the mass of the particle.

At $(x_0,0,0)$speed of the particle is $\sqrt{4^2+3^2}=5$ units

Using Work -Energy Theorem, we get

$\left(q{E}_0\right)x_0=\frac{1}{2}m{v}^2=\frac{25m}{2}$

$\Rightarrow x_0=\frac{25m}{2q{E}_0}$