Problem:
A spherical shell of radius 1.5 cm has a charge of 20 microcoloumb uniformly distributed over it. What is the force exerted by one half over the other half?

Solution:

Given:
- Radius of the spherical shell, r = 1.5 cm = 0.015 m
- Charge uniformly distributed over the shell, Q = 20 μC = 20 × 10^(-6) C

Approach:
To find the force exerted by one half of the spherical shell on the other half, we can consider the problem as two point charges located at the center of each hemisphere of the sphere. We will calculate the force between these two point charges using Coulomb's law and then double the value to account for the entire spherical shell.

Calculating the Charge:
The charge distributed over the spherical shell can be considered as two hemispheres with equal charge. Therefore, the charge of each hemisphere, Q_hemisphere = Q/2 = 10 × 10^(-6) C.

Calculating the Force:
To calculate the force between the two hemispheres, we use Coulomb's law:

F = (k * q1 * q2) / r^2

where F is the force, k is the electrostatic constant (9 × 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

Calculating the Electrostatic Constant:
Substituting the given values into the equation, we get:

k = (9 × 10^9 Nm^2/C^2)

Calculating the Distance:
Since the charges are located at the center of each hemisphere, the distance between them is equal to the radius of the spherical shell, r = 0.015 m.

Calculating the Force between the Hemispheres:
Substituting the values into Coulomb's law equation, we get:

F_hemisphere = (k * q1 * q2) / r^2

Calculating the Total Force:
To find the force exerted by one half of the spherical shell on the other half, we need to double the force between the hemispheres since there are two hemispheres in the shell.

F_total = 2 * F_hemisphere

Final Answer:
Calculate the value of F_total using the above equations to find the force exerted by one half of the spherical shell on the other half.