List of top Physics Questions on Motion of charged particles in a magnetic field

A charged particle is moving in a uniform magnetic field \( \vec{B} \) with a constant speed \( v \) in a circular path of radius \( r \). Which of the following graphs represents the variation of radius of the circle, with the magnitude of magnetic field \( \vec{B} \)?
A proton moving with velocity \( V \) in a non-uniform magnetic field traces a path as shown in the figure. The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q, and R? What can you say about relative magnitude of magnetic fields at these points?
proton moving with velocity V in a non-uniform magnetic field
A charged particle is moving in a circular path with velocity \( V \) in a uniform magnetic field \( \vec{B} \). It is made to pass through a sheet of lead and as a consequence, it looses one half of its kinetic energy without change in its direction. How will (1) the radius of its path change? (2) its time period of revolution change?
A particle having charge \( +q \) enters a uniform magnetic field \( \vec{B} \) as shown in the figure. The particle will describe:
A particle having charge
A proton and an \( \alpha \)-particle enter with the same velocity \( \vec{v} \) in a uniform magnetic field \( \vec{B} \) such that \( \vec{v} \perp \vec{B} \). The ratio of the radii of their paths is:
A particle of mass \( m \) and charge \( q \) moving with velocity \( \vec{v} = v \hat{i} \) is subjected to a uniform electric field \( \vec{E} = E \hat{j} \). The particle will initially have a tendency to move in a circle of radius:
A particle of specific charge \( \frac{q}{m} \) is projected from the origin towards the positive x-axis with the velocity \( 10 \, \text{m/s} \) in a uniform magnetic field \( B = -2 \hat{k} \, \text{T} \). The velocity \( v \) of the particle after time \( t = 5 \, \text{ms} \) will be (in m/s)
A particle of mass \( m \) and charge \( q \) describes a circular path of radius \( R \) in a magnetic field. If its mass and charge were \( 2m \) and \( \frac{q}{2} \) respectively, the radius of its path would be: