F m (a) v . The direction of F m on negative charge is opposite to the direction of F m on positive charge provided other factors are identical as shown Figure . (b) . If velocity v of the charge q is along magnetic field B then, F m is zero Definition of tesla The strength of the magnetic field is one tesla if a unit charge moving normal to the magnetic field with unit velocity experiences unit force.
T= 1Ns Cm = N A m =1N A m EXAMPLE . A particle of charge q moves with velocity v along positive y - direction in a magnetic field B . Compute the Lorentz force experienced by the particle (a) when . LORENTZ FORCE When an electric charge q is kept at rest in a magnetic field, no force acts on it.
At the same time, if the charge moves in the magnetic field, it experiences a force. This force is different from Coulomb force, studied in unit . This force is known as magnetic force. It is given by the equation v ( .
) In general, if the charge is moving in both the electric and magnetic fields, the total force experienced by the charge is given by q E + × v . It is known as Lorentz force. . .
Force on a moving charge in a magnetic field When an electric charge q is moving with velocity v in the magnetic field B , it experiences a force, called magnetic force F m . After careful experiments, Lorentz deduced the force experienced by a moving charge in the magnetic field F m m = v ( . ) In magnitude, q B m = v sin θ ( . ) The equations ( .
) and ( . ) imply . F m is directly proportional to the magnetic field . F m is directly proportional to the velocity v of the moving charge 12th - 12th - - - - - Unit Magnetism and magnetic effects of electric current (c) Magnetic field is in zy - plane and making an angle θ with the velocity of the particle, which implies j k cos sin θ θ z ν + q x y From Lorentz force, j j k m = ( ) × v v ( cos sin Bsin θ θ θ EXAMPLE .
Compute the work done and power delivered by the Lorentz force on the particle of charge q moving with velocity v . Calculate the angle between Lorentz force and velocity of the charged particle and also interpret the result. Solution For a charged particle moving on a magnetic field, v The work done by the magnetic field is W F dr dt