physics

The electric field a height R above the center of a line charge of length L is . This is the result of the integral that we derived in class for the electric field above a finite line. The direction of the electric field is the direction connecting the center of the line to the point of measurement.

Z

L

L/2

P

2

3

1

z

y

4

x

Consider the above charged line, twisted into a square shape with four sides, 1,2,3,4 in the x-y plane, of side length L.

a) Find, using symmetry, the direction of the electric field at point P above the center of the square. (hint, how do the fields due to the four sides add up?)

b) What is the electric field at point P due to side 1? Express it in terms of its x and z components.

c) Using parts a) and b), what is the total electric field at point P?