Question

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by p(r) = kr, where r is the distance from the centre two charges A and B of –Q each are placed on diametrically opposite points, at equal distance a form the center. If A and B do not experience force, then:

A. a = 3R/ 1/4
B. a = 2R/√3
C. a = 8 − 1/4R
D. a = 2 − 1/4R

Answer 1

The value of a that satisfies the condition that charges A and B do not experience force is 0.

Step-by-step explanation:

The problem involves finding the value of a such that two charges of -Q each, placed at diametrically opposite points on a sphere with charge density given by p(r) = kr, do not experience any force. We can approach this problem by considering the electric field created by the charge distribution and equating it to zero at the location of charges A and B.

Using Gauss's Law, we find that the electric field at a distance r from the center of the sphere is given by E(r) = (kr²)/(3ε₀), where ε₀ is the permittivity of free space. Setting the electric field at distance a from the center of the sphere to zero, we get (ka²)/(3ε₀) = 0. Solving for a, we find that a = 0 (since k, ε₀, and a cannot be zero). Therefore, there is no value of a that satisfies the condition that charges A and B do not experience force.