Question

A particle of specific charge $\alpha$ 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 $(x_0,y_0,0)$ is $(4\hat{i}+3\hat{j})$. The value of $x_0$ is

• A. $\frac{16\alpha B_0}{E_0}$
• B. $\frac{13\alpha E_0}{2B_0}$
• C. $\frac{25}{2\alpha E_0}$
• D. $\frac{5\alpha }{2B_0}$

Answer 1

The correct option is C

$\frac{25}{2\alpha E_0}$

From work-energy theorem, $\Delta W_E+\Delta W_B=\Delta K$
$\Rightarrow q{E}_0{x}_0+0=\frac{1}{2}m{v}^2=\frac{1}{2}m(3^2+4^2)$
$\Rightarrow \frac{q}{m}{E}_0{x}_0=\frac{25}{2}$
$\Rightarrow \alpha E_0{x}_0=\frac{25}{2}$
$\therefore x_0=\frac{25}{2\alpha E_0}$