Question

A magnetic field
A. Always exerts a force on a charged particle
B. Never exerts a force on a charged particle
C. Exerts a force, if the charged particle is moving across the magnetic lines of force
D. Exerts a force, if the charged particle is moving along the magnetic lines of force

Answer 1

Hint: In the given question, we need to determine whether the magnetic field exerts a force or not in certain conditions. For this, first we will define the magnetic field. For this, we need to use the formula for force experienced by a charged particle in an external magnetic field to get the desired result.


Formula used:
The following formula is used for solving the given question.
Magnetic force experienced by a charged particle is \[\vec F = q(\vec v \times \vec B)\].
Here, \[F\] is the force, \[B\] is the magnetic field, \[q\] is the charge of a particle and \[v\] is the velocity.



Complete answer:
We know that the magnetic force experienced by a charged particle is \[\vec F = q(\vec v \times \vec B)\].
Here, \[F\] is the force, \[B\] is the magnetic field, \[q\] is the charge of a particle and \[v\] is the velocity.
So, consider the following figure for this.

Image: Direction of cross product of magnetic field and velocity
We can define it as \[F = qvB\sin \theta \]
Here, we can say that If \[{\bf{v}}\parallel {\bf{B}}\] then only \[{\bf{F}} = {\bf{0}}\].
Thus, the velocity is parallel to the magnetic field line means the value of \[\sin \theta \] is zero.
This indicates that \[\theta = {0^o}\].
As a result, the magnitude of force is non-zero only if a charged particle moves across the magnetic field lines of forces.
Therefore, the correct option is (C).





Note: Many students forget to write an expression for the magnetic force experienced by a charged particle. They may give the explanation without the formula but it will not give a clear idea about the condition. This is the only way through which we can solve the example in the simplest way.