Question

a thin spherical shell of radius r is divided into two equal halves, and each half is charged with the same uniform surface charge density σ, what is the relationship between the force F required to keep the halves in equilibrium and the given parameters?

Answer 1

The relationship between the force required to keep the halves of a charged spherical shell in equilibrium and the given parameters is F α q^2/r^2.

Step-by-step explanation:

To find the relationship between the force F required to keep the halves of the charged spherical shell in equilibrium and the given parameters, we can use Coulomb's Law and the concept of electric field.

Each half of the shell will experience a repulsive force from the other half due to the charges. This force can be calculated using Coulomb's Law: F = k * (q1 * q2) / r^2, where k is the Coulomb's constant, q1 and q2 are the charges on the two halves of the shell, and r is the radius of the shell.

Since each half of the shell has equal charge q and the radius of the shell is r, the force between them can be written as F = k * (q * q) / r^2. Simplifying this expression, we get:

F = (k * q^2) / r^2

Therefore, the relationship between the force F and the given parameters is F α q^2/r^2.