Question

1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result to find the contribution to the dipole moment from a circular slice of the dise with radius s, height h and width ds (as showm). This will take the usual form of dipole moment (current around a loop) × (area of loop) The full dipole moment of the disc you are trying to determine is qwa Even if you are unable to reproduce this result, you can still use the correct result for m in parts (b) and (c) ds b) Consider a circular loop of radius Ro around the z-axis at height z0 above the disc for the case R0 《a 《 . Find the magnetic flux through the loop, and hence find the vector potential at the loop (c) If, due to friction in the axle, the disc's angular velocity is decreasing exponentially with time t as w(t) woe '/to, where to is the decay time scale, find the electric field at the loop at time t-0· [Hint: use the relationship between E and the time-derivative of A

Answer 1

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