Question

A charged particle goes undeflected in a region containing electric and magnetic fields. It is possible that:
A) $\vec E\parallel \vec B, \vec V \parallel \vec E$.
B) $\vec E$ Is not parallel to $\vec B$.
C) $\vec V \parallel \vec B$ but $\vec E$ is not parallel to $\vec B$.
D) $\vec E \parallel \vec B$ but $\vec V$ is not parallel to $\vec E$.

Answer 1

The charges particle present in the electric field experiences force of which deflects the particle from the field. The charged particle in the presence of a magnetic field experiences a force due to which the particle deflects and cannot continue its original path.

Complete step by step answer:
It is given that the charged particle goes undeflected in a region containing electric as well as magnetic field and we need to tell which is the perfect condition for the charged particle to remain undeflected.

Here in this problem it is not given in which direction the magnetic and electric field is applied also the direction of motion of the particle is also not given so we can find the best possible condition for which the particle will not get deflected.

We will consider each option one by one and tell which option is correct for the given condition.

Option A.
$\vec E\parallel \vec B, \vec V \parallel \vec E$
Here we can see that the velocity vector magnetic vector and electric field vector all are parallel to each other $\vec E\parallel \vec B\parallel \vec V$. The charged particle will not experience any force due to the magnetic field as the angle between the magnetic field and velocity vector is zero or we can say that the velocity vector and magnetic vector are parallel. The force applied by the electric field on the charged particle will also be zero as the velocity vector is parallel to the electric field vector.

Option B,
$\vec E$ is not parallel to $\vec B$.
If the electric field is not parallel to the magnetic field then let us assume that a condition that the magnetic field is coming out of the paper and the electric field and velocity vector makes a right angle. Then the force applied by the magnetic field can be cancelled by the force applied by the electric force on the charged particle so the particle moves undeflected.

Option C,
$\vec V \parallel \vec B$ but $\vec E$ is not parallel to $\vec B$.
Here in this option it is given that the velocity is parallel to the magnetic field which means no force on the particle due to magnetic field and also the electric field and magnetic field both are not parallel which means there will definitely be some force on the particle due to electric field. so the particle will get deflected.

Option D,
$\vec E\parallel \vec B$ but $\vec V$ is not parallel to $\vec E$.
Here in this option the electric and magnetic fields are parallel but the velocity is not parallel to any of the field, so particles will get deflected due to the presence of electric and magnetic fields and as both of them are not parallel to the velocity of the particle.

After considering all the options option A and option B are the correct answers for this problem.

Note: In some options the placement of magnetic and electric fields determines whether the particle will get deflected or not so if any of the case in the above options gets the particle deflected then that option is taken as not the correct option for the problem.