Question

Two Spheres A and B having radii in the ratio 1 ratio 2 are connected together with the conducting wire the ratio of their surface charge densities σA/σB will be? a 1/2 b 2 c 1/4 d 4

Answer 1

Answer:

b2 will be the answer in my study please make me brainlist

Answer 2

The correct answer is (d) 4.

Given:

Two Spheres A and B having radii in the ratio 1 ratio 2 are connected together with the conducting wire the ratio of their surface charge densities σA/σB

To Find:

σA/σB = ?

Solution:
The ratio of the surface charge density of sphere A to that of sphere B can be found using the conservation of charge principle. Since the two spheres are connected together with a conducting wire, they will share charge until they reach a common potential. The charge on each sphere is directly proportional to its surface area, and the potential difference between the two spheres is zero. Therefore, the charges on the two spheres must be equal.

Let the radius of sphere A be r and that of sphere B be 2r. The surface area of a sphere is given by 4πr^2, so the surface area of sphere A is 4πr^2 and that of sphere B is 4π(2r)^2 = 16πr^2.

Let the surface charge density of sphere A be σA and that of sphere B be σB. Then the charge on sphere A is Q = 4πr^2σA and the charge on sphere B is Q = 16πr^2σB.

Since the two spheres have equal charge, we have:

4πr^2σA = 16πr^2σB

Simplifying, we get:

σA/σB = 16/4 = 4

Therefore, the ratio of the surface charge density of sphere A to that of sphere B is 4:1, or σA/σB = 4/1. Answer: d) 4.


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