Charge particle in magnetic field

A point charge moving in uniform magnetic field experiences a force on . Behaviour of charge particle depends on the angle ‘θ ‘ between .

Case 1, if θ = 0⁰ or 180⁰

When the charged particle  moves  parallel or anti parallel to field then no net force acts on it & its trajectory remains a straight line.

Case 2, If θ is other than 0⁰, 180⁰ & 90⁰  

Charge particle moves in a helical path of radius , completes one circle in time & travels a distance in one time period in the direction of field called pitch & is given by,

Case 3, If θ is 90⁰

Charge particle moves in a circle at uniform speed.

Radius of circular path is

KE of particle is constant. It completes a cycle in time  at angular frequency .

As the force acting on the particle is only normal & no tangential force is available thus speed & hence KE also of the particle will remain unchanged. As the kinetic energy of the charged particle remains constant. Hence no work is done in moving a charge particle moving at right angles to the magnetic field. However due to change in direction  &  are variables in direction.

^Displacement

Suppose a body is moving along a straight line. Let the straight line is along x – axis. Let at a time t₁ it was situated at point A at a distance x₁ from a fixed point O. Let it moves & at time t₂ reaches point B situated at a distance x₂ from O.

Here the distance AB is called displacement of the body along x axis (S_x) in the time interval t₂ – t₁ (= Dt). In terms of position coordinates it can be expressed as

Displacement, AB = OB – OA = x₂ – x₁ or Δx.

i.e. for motion along displacement is equal to the change in position coordinates along that line.