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 , 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 ₀ 4 Q R^2 z^3 . The value of n is:

Step-by-step solution

For a point on the axis at a distance z R and z h , the rotating cone can be considered as a magnetic dipole. The magnetic field on the axis of a dipole is given by: B = ₀ 4 2M z^3 where M is the magnetic dipole moment of the cone. To find M , consider an elemental ring on the cone at a vertical distance y from the origin, with vertical thickness dy . The radius of this ring is r = R h y and its slant length is dl = R^2+h^2 h dy . The surface charge density of the cone is = Q R R^2+h^2 . The charge on the elemental