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# Electric Potential and Electric field

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(See attached file for full problem description with diagram)

(1) Two point charges, Q1 = +2 x 10-6 C and Q2 = -3 x 10-6 C, are situated as shown. (Refer to the attached file to view the diagram)

(a) Find the electric potential at point A and at point B.
(b) Find the work needed to move a point charge Q3 = 5 x 10-6 C from point A to point B along the curved path shown by the solid line

(2) A solid, insulating sphere of radius a has a uniform charge density &#961; and a total charge +Q. Find the magnitude of the electric field in the regions r<a and r>a . Draw the schematic graph of electric field (E vs. r).

##### Solution Summary

Two questions involving point charges and a uniformly charged sphere have been answered. Each step in finding the potential energy and electric field inside and out side of a uniformly charged sphere has been shown. A sketch of electric field vs. radius is included as well. Students can study the techniques used here to solve similar problems.

##### Solution Preview

No. 1

Two point charges, Q1 = +2 x 10-6 C and Q2 = -3 x 10-6 C, are situated as shown.
a) Find the electric potential at point A and at point B.
b) Find the work needed to move a point charge Q3 = 5 x 10-6 C from point A to point B along the curved path shown by the solid line.

V = k q/r
Where k = 8.99 X 10^9 N/m^2/C^2
VA= k (Q1/2 + Q2/2) = 8.99 X 10^9(1x 10-6 - 3/2 x 10-6 ) = -4.49 x 10^3 V
VB= k ...

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