What is the electric field strength at the midpoint between the two spheres?

Question

Two 2.0-cm-diameter insulating spheres have a 5.90 cmcm space between them. One sphere is charged to + 55.0 nCnC , the other to - 52.0 nCnC .

Answer 1

Step 1:

Diameter of the two spheres is .

Radius of the sphere is .

Charge on first sphere is .

Charge on second sphere is .

Distance between the two spheres is .

Total distance from center of the sphere to the mid point is .

.

Electric field due to charged particle is , where

is the permittivity of free space .

is the charge of the electron.

is the distance between the two point charges.

Find the electric field strength of the first sphere.

Substitute , and .

.

The electric field strength of the first sphere is .

Step 2:

Find the electric field strength of the second sphere.

Substitute , and .

.

The electric field strength of the second sphere is .

Since mid point is considered, the magnitude of the right sphere contribution is also same as the left sphere and is in oppsit direction.

.

Solution :

Electric field strength at the midpoint between the two spheres is .