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Force on a Charged Particle in Magnetic Field

If a particle carrying a positive charge q and moving with velocity v enters a magnetic field B, then it experiences a force F which is given by the expression
where 81521.png velocity of the particle, 81527.png magnetic field and θ = angle between velocity vector and magnetic field vector.

Zero force

Zero force Force on charged particle will be zero (i.e., F = 0) if
  • No field, i.e., B = 0 ⇒F = 0
  • Neutral particle, i.e., q = 0 F = 0
  • Rest charge, i.e., v = 0 F = 0
  • Moving charge, i.e., θ = 0o or θ = 180o F = 0

Direction of force

The force 81533.png is always perpendicular to both velocity 81539.png and field 81545.png in accordance with right hand screw rule, though 81551.png and 81557.png themselves may or may not be perpendicular to each other (Fig. 1).
Fig. 1
The direction of force on a charged particle in magnetic field can also be found by Fleming’s left hand rule (FLHR).
Here, first finger (indicates) Direction of magnetic field.
Fig. 2
Middle finger Direction of motion of positive charge or direction, Opposite to the motion of negative charge.
Thumb Direction of force (Fig. 2).

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