Question

AZ The figure shows a solid spherical conductor of radius R placed a height d directly above the centre of a square conducting plate of area A. The sphere has a net charge of +Q and the plate has a net charge of -Q, and the system is in electrostatic equilibrium (a) Sketch the equilibrium charge and field distributions. Describe two characteristics of the charge and field configurations of conductors in equilibrium as illustrated by your sketch. For the remainder of the question, you may approximate the charge distributions on both the sphere and plate as uniform. You may also neglect fringing fields at the edges of the plate, treating it as a section of an infinite plate (b) Discuss in what regimes you would expect these approximations to be reasonable (c) Write down the electric field of the combined system along the z-axis between the sphere and the plate. (d) Calculate the capacitance of the system. You may use the result that the electric potential between 0< <d - R on the z-axis is given by where Vo is a constant, and z 0 on the plate

C and D please !  

Answer 1

Given that A solid spherical conductor of radius R height d. plate of area A. Net charge is + Q, - Q (c) Rightarrow since the charge reside only the surface of the conductor the field lines are perpendicular to the surface because of vector addition of the fields. Rightarrow According to Gauss Law the surface does not enclose any charge Rightarrow By Gauss law and symmetry, the electric field inside the sphere is Zero (d) Given that the electric potential between 0 < z < d - R on the Z-axis. \r\n The capacitance of the system is given by c = q/v the charge here is q = Q Potential V is given, Therefore c = Q/V_0 + Q/2E_0[1/2 pi (d - Z) + Z/A] where V-0 is constant z = 0 in the plane