Force On A Moving Charge

Card # 67‐Force on a moving charge in a uniform magnetic field Experimental observation show that when a charge moves in a magnetic field it experiences a

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force called Lorentz force. If a charge q is moving with velocity V in a magnetic field of

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strength B , making an angle θ with the direction of B than the magnetic force acting on moving charge is 1. Directly proportional to magnitude of charge

Fmα q

2. It is directly proportional to the strength of magnetic field

Fmα q

3. It is directly proportional to component of velocity perpendicular to the magnetic field

FmαV sin θ

Combining above results Fmα qVB sin θ or Fm = kqVB sin θ Where k is a proportionality constant in SI system K =1 Therefore magnetic force

Fm = qVB sin θ

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In vector form Fm = qV × B

 

Force on a moving charge in simultaneous electric and magnetic fields: Lorentz force

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If a particle enters in a region in which both electric E and magnetic field B are present

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Then total force F = Fe + Fm

ur ur ur ur F = qE + q(V × B ) ur ur ur ur F = q( E + V × B)

This equation is called Lorentz force equation