Problem 19.

An electrostatic field is given by  

Determine the work done in moving the charge

(a) from (0,0,0) to (4,0,0) m

(b) from (4,0,0) to (4,2,0) m

(c) from (4,2,0) to (0,0,0) m along a straight path.

Solution

If the charge is moving from point A to point B then the work done by electric field is given by the expression:

In this expression the integral is calculated along any trajectory connecting points A and B.

(a) We calculate the integral along the straight line connecting initial and the final points:

(b) We calculate the integral along the straight line connecting initial and the final points:

(c) We calculate the integral along the straight line connecting initial and the final points: