Let $\vec{E}$ and $\vec{B}$ 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:

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$\vec{E} \neq 0 and \vec{B} = 0$

$\vec{E} \neq 0 and \vec{B} \neq 0$ both $\vec{E}$ and $\vec{B}$ are parallel to $\vec{v}$

$\vec{E} = 0 and \vec{B} = 0$

$\vec{E}$ is parallel to $\vec{v}$ but $\vec{B}$ is perpendicular to $\vec{v}$

answer is A, B, C.

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Detailed Solution

If a charge particle experiences no electromagnetic force, then electric field must be zero (as $\vec{F} = q \vec{E}$ ). The magnetic field may or may not be zero as a charge particle at rest or moving in the direction of magnetic field experiences no force.

(a) When both $\vec{E}$ and $\vec{B}$ are 0, it is undeflected.
(b) If $\vec{E}$ is non-zero and B=0, it will move in the direction of E and remains undeflected.
(c) $\vec{E}$ is non-zero, force will be in direction of E. B is non-zero and V is parallel to $\vec{B}$ .
(d) $\vec{F} = q \vec{v} \times \vec{B}$ will not be zero due to $\vec{B}$ and proton will not move in the direction of $\vec{E}$ because of $\vec{F}$ .