A charge Q is uniformly distributed over the surface of non conducting disc of radius R . The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity . As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radiu

Step-by-step solution

Consider ring like element of disc of radius r and thickness dr . If is charge per unit area, then charge on the element d q= (2 r d r) current ' i ' associated with rotating charge dq is i = ( dq ) w 2 = wrdr Magnetic field dB at center due to element dB = ₀ i 2 r = ₀ dr 2 aligned & B _ net = dB = ₀ 2 ₀^ R dr = ₀ R 2 & B _ net = ₀ Q 2 R [ Q = R ^2 ] aligned So if Q and w are unchanged then B _ net 1 R Hence variation of B_ net with R should be a rectangular hyperbola as represented in (A).