A hollow, right circular cone of base radius R and height h, with its tip at the origin is rotating about the Z-axis with an angular velocity ω, as shown in the figure. The cone carries a total charge Q uniformly distributed on its curved surface. The magnitude of magnetic field at a point (0,0,z), where z ≫ R and z ≫ h, is n μ₀QR²ω/(4πz³). The value of n is:

Question

G1 Physics · Accepted Answer

For a distant point on the axis, the rotating charged cone behaves like a magnetic dipole. Integrating the magnetic moment of concentric charged rings over the conical surface gives m = QR²ω/4. The far axial field is B = μ₀(2m)/(4πz³) = (1/2) μ₀QR²ω/(4πz³). Hence n = 0.50.