Question

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left( \frac{v_o}{\sqrt{2}} \hat{x} + \frac{v_o}{\sqrt{2}} \hat{y} \right)$. There exists a uniform magnetic field $\vec{B} = B_o \hat{z}$ and a space varying electric field $\vec{E} = E_o e^{-\lambda x} \hat{x}$ within the region $0 \le x \le L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is \dots

• A. $\frac{q E_o}{\lambda} [ 1 - e^{-\lambda L} ]$
• B. $\left( \frac{v_o q B_o}{2 \lambda} \right) [ 2 - e^{-2\lambda L} ]$
• C. $\frac{q E_o}{\lambda} [ 1 + e^{-\lambda L} ]$
• D. $q \left( \frac{E_o + v_o B_o}{\lambda} \right) [ 1 - e^{-\lambda L/2} ]$

Answer 1

The Correct Option is A