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.

Question

Physics

Mitchell Wilkerson

17 January, 20:50

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.

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Lala · Answer 1

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)