force

Example 1:

           An insulating circular disc of radius a = 20 cm has a uniformly distributed static charge of surface density s = p Cm^–2. The disc rotates about its centre with an angular velocity                 w =100rad/s. Find the magnetic field at the centre of the disc. ( p² = 10)

Solution:

           The disc may be considered to be made up of concentric circular rings with radius increasing from 0 to a. Consider one such elementary ring of radii r and r + dr.

           Face area  =

           Charge      =

          Angular velocity =

           Period   

The elementary charge when the disc rotates to equivalent to a circular current loop. The amount of charge passing through the current loop during T =

           \          I  =

                           =  

           Magnitude of magnetic field at centre dB =             =

           \        total magnetic field due to all rings =  =  = 40 mT