A dielectric circular disc of radíus R carries a unform surface charge density . If it rotates about its axis with angular velocity , the magnetic fíeld at the cente of dísc is :

Step-by-step solution

Let us assumed a ring like element of the disc of radius r and thickness d r . If is the surface charge density, then the charge on the element. d q= (2 r) d r Current d i associated with rotating charge d q is d i= d q T = d q 2 ( T= 2 ) From Eqs. (i) and (ii), we get d i= r d r As, the magnetic field d B at centre due to the element, aligned & d B= ₀ d i 2 r = ₀ r d r 2 r d B= ₀ 2 d r & B_ net = ₀ 2 ₀^R d r B_ net = ₀ R 2 & aligned Hence, the correct option is (2).