Question

Suppose a charged particle moves with a velocity v near a wire carrying an electric current. So, a magnetic force acts on it. If the same particle is seen from a frame moving with velocity v in the same direction, the charge will be found to be at rest. Will the magnetic force become zero in this frame? Will the magnetic field become zero in this frame?

Answer 1

In this frame of reference, the particle is at rest, so that magnetic force becomes zero. there is a positive charge flow.

The magnetic field also exists, which must not be zero.

Explanation:

Step 1:

In the reference frame, magnetic force becomes zero. This is due to the reason that the particle is at rest.

The force on a particle is $F=q v B \sin (\theta)$

where the particle’s velocity is v.

When F = 0 and v = 0.

On the particles, still exist the magnetic field. This is due to the fact that the current is not dependent on the reference frame. In a wire, if the electrons are at rest in a reference frame, the protons flow still opposite to the reference frame. The magnetic and current fields still exist because of this.

Step 2:

Given,

It is given that the magnetic force is  $F=q v B \sin \theta$  

Where q is the electric charge, which is  $1.6 \times 10^{-19} \mathrm{C}$

Magnetic force is denoted as F

Velocity is v.  

Step 3:

Near the conducting wire, a charge particle is moving along with the frame in the same direction. It is known from the frame that there is resting of the charge. Hence, the charge particle’s velocity is zero. So, the value of magnetic force is zero.

The current will be zero when the charge is at rest. So, the magnetic field should not be zero.