A proton is propelled with a constant velocity ' v ' along the axis of a current-carrying solenoid, and then

When a charged particle moves in a magnetic field, a force acts on the charge particle; this force is known as a magnetic force.

The magnetic force on a charged particle of charge q and velocity V in a magnetic field B is given by:

$\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})=qVBSin\theta$It is the cross-product of the velocity vector $\overrightarrow{V}$ and magnetic field vector $\overrightarrow{B}$ where $\theta$ is the angle between velocity and magnetic field.

The magnetic field in the solenoid runs down the axis of the solenoid.

Because the proton was projected along the axis, the angle between the magnetic field and velocity is zero.

Here $\theta =0°$

Force on proton $\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})=qVBSin\theta =qVBSin0=0$

As there is no force acting on the proton, it will continue to flow down the axis at the same velocity v.