Question Problem 3. A spherical shell with radius R and uniform surface charge density o, rotates with angular velocity w about the z axis, which passes through its center. (a) Use the Biot-Savart law to show that the contribution to the magnetic field at the center of the sphere made by a thin ring of the surface located at polar angle 0 with an angular width do is dB = žu00 .wR sin’ do. (b) Find the total magnetic field at the center by integrating this expression over 6 from 0 to it.
Given, Ansulervelsity =omega.:. Time, T=2pi//w_(i).a charge on the elementary ring Shown in the figure,{:[d*theta=sigma_(0)xx ds],[=sigma_(0)xx2pi R*sin theta Rd theta.],[d theta=2piR^(2)sigma_(0)sin theta d theta]:}∴=dI= current due to this segment,dI=(dQ)/(T)=(dQ)/((2pi)/(omega))=omegaR^(2)sigma_(0)sin theta d theta.from Bio. Savart law, magnetic field at centre due to thins current ring,{:[d vec(B),= hat(z)(mu_(0))/(4pi)*(2pi(dI)*(AP)^(2))/((AP^(2)+A0^(2))^(3//2))*],[,= hat(z)*(mu_(0))/(2)sigma_(0)omega*(R^(2)sin theta d theta*R^(2)sin^(2)theta)/((R^(2)sin^(2)theta+R^(2)cos^(2)theta)^(3//2))],[R,Rsin^(3)theta d theta]:}{:[= hat(z)(mu_(0))/(2)sigma_(0)omega*(R4sin^(3)theta d theta)/(R^(3))],[d vec(B)= hat(z)(1)/(2)mu_(0)sigma_ ... See the full answer