Question

What should be the charge on a sphere of radius 2 cm so that when it is brought in contact with another sphere of radius 5cm carrying a charge of 10 microcoulomb, there is no net transfer of charge between the spheres.

Answer 1

The charge on a sphere of radius 2 cm so that when it is brought in contact with another sphere of radius 5 cm carrying a charge of 10 micro coulombs is 4 * 10⁻⁶ C.

Explanation:

We are given that there is no net transfer of charge between the spheres, so, both the spheres will have same potential energy which is denoted as “V”.

Step 1: For the sphere of radius, r1 = 5 cm = 0.05 m

Charge for the this sphere is given, q1 = 10 µC = 10 * 10⁻⁶ = 10⁻⁵ C

The potential energy “V” is given as,

V = [Kq1] / r1 …… [columbs constant K = 9 * 10⁹ Nm²/C²]

⇒ V = (9 x 10⁹ x 10⁻⁵) / 0.05

⇒ V = 1.8 * 10⁶ V

Step 2: For the sphere of radius, r2 = 2 cm = 0.02 m

Let the charge on the sphere of radius 0.02 m be denoted as “q2” Columb.

Thus,  

The charge “q2” on the sphere of radius 0.02 m will be,

= [V * r2] / K

= [1.8 * 10⁶ * 0.02] / 9 x 10⁹

= 4 * 10⁻⁶ C