Question

Let $\overrightarrow{E}$ and $\overrightarrow{B}$ denote the electric and magnetic fields in a certain region of space. A proton moving with a velocity along a straight line enters the region and is found to pass through it undeflected. Indicate which of the following statements are consistent with the observations

• A. $\overrightarrow{E}=0$ and $\overrightarrow{B}=0$
• B. $\overrightarrow{E}\ne 0$ and $\overrightarrow{B}=0$
• C. $\overrightarrow{E}\ne$ and $\overrightarrow{B}\ne 0$ and both $\overrightarrow{E}$ and $\overrightarrow{B}$ are parallel to $\overrightarrow{v}$
• D. $\overrightarrow{E}$ is parallel to $\overrightarrow{v}$ but $\overrightarrow{B}$ is perpendicular to $\overrightarrow{v}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\overrightarrow{E}\ne 0$ and $\overrightarrow{B}=0$
B $\overrightarrow{E}\ne$ and $\overrightarrow{B}\ne 0$ and both $\overrightarrow{E}$ and $\overrightarrow{B}$ are parallel to $\overrightarrow{v}$
C $\overrightarrow{E}=0$ and $\overrightarrow{B}=0$

a) When both $\overrightarrow{E}$ and $\overrightarrow{B}$ are zero, the particle is undeflected.
b) When $\overrightarrow{E}\ne 0$ and $\overrightarrow{B}=0$, the particle will move in the direction of $\overrightarrow{E}$ and remains undeflected provided $\overrightarrow{E}\parallel \overrightarrow{v}$.
c) $\overrightarrow{E}\ne 0$, $\overrightarrow{B}\ne 0$ $\overrightarrow{E}\parallel \overrightarrow{v}$ and $\overrightarrow{B}\parallel \overrightarrow{v}$. Hence, there is no deflection due to magnetic field and particle will accelerate or decelerate in the direction of $\overrightarrow{v}$.
d) The particle will be deflected since $\overrightarrow{v}\perp \overrightarrow{B}$.