Question

Determine an expression for the electric potential V on the sphere's surface. Express your answer in terms of some or all of the variables R, q. Use k for the constant from Coulomb's law.

Answer 1

Answer:

V = k*q / R

Explanation:

Given:

- Radius of the solid sphere: R

- Coulombs constant: k

- charge on the sphere: q

Find:

Electric potential V at the surface of sphere.

Solution:

- We apply Gauss Law to determine the Electric field strength of the charged sphere:

                        Q_enclosed / e_o = surface integral (E) .dA

- The surface integral of Electric field strength E is given by:

                        E.dA = E.(4*pi*r^2) = q_enclosed / e_o

- Hence

                                       E =  q_enclosed /4*pi*r^2 *e_o

- Where                           k = 1 / 4*pi*e_o

Hence,                             E = k*q / r^2

- Next we compute Electric Potential V:

                                       V = integral (E) .dr

                                       V = integral( k*q / r^2) . dr

                                       V = k*q integral(1 / r^2) . dr

- Integrate the expression from R < r < infinity

                                        V = - k*q * (1 / r)

                                        V = -k*q*( 0 - 1 / R)

                                        V = k*q * (1 / R)