Question

Eight electrons (-e) located on the corners of a cube. Length of side of cube is 2m. (+2e) charge is located at the center of cube as in figure. What is the electric potential energy of this system? If the electric potential energy of this system is positive or negative, please explain this result using work-energy theorem. (e=1.602×10−19 Coulombs)

Answer 1

Explanation:

Side of the cube =a

Length of each diagonal =

a

2

+a

2

+a

2

=

3

a

Distance of each corner from centre O= half the diagonal =

2

3

a

Potential at O due to charge at each corner =

4πε

o

1

3

2

a

q

=

4πε

o

1

3

a

2q

Therefore, net potential at O due to all the 8 charges at the corners of the cube,V=8×

4πε

o

1

3

a

2q

=

4πε

o

1

a

3

16q

The electric field at O due to charges at all the corners of cube is zero, since, the electric fields due to charges at opposite corners such as A and H, G and E, F and C are equal and opposite.