Question

Two tiny conducting spheres are charged and set 4.1 mm apart. The first sphere has a charge of 6.3 mC on it, and feels a force of 1800 N towards the second sphere.

a. Does the second sphere have a positive or negative charge? Why?

b. What is the magnitude of the charge on the second sphere? [0.53 mC]

Answer 1

a) The second sphere has a negative charge.

Because of the first sphere has a positive charge and other have an opposite charges hence the second sphere has negative charge.

b) Given

r = 4.1 mm = 4.1 × 10^-3 m

Force = 1800 N

First sphere has charge = 6.3 mC

q₁ = 6.3×10^-6 C

q₂ = ?

K = 9× 10⁹

According to coloumbs law ,

F= K [(q_1×q₂)/r² ]

q_{2 =} [Fr² /q₁ ] ×K

q_{2 =} [1800 × (4.1×10^-3)² × 9×10 ⁹ ] / (6.3×10^-6)

q_{2 =}[ 1800 ×(4.1)²  × 10^-6]/ (9× 6.3× 10^-6)

q_{2 =} 30258÷( 9×6.3)

q_{2 =} 533.650

q_{2 =} 0.533mC

The magnitude of charge on second sphere is 0.553mC

When the two conducting sphere are brought together to touch, it is as though they become one single big conductor and the total charge of the two sphere out across the whole surfaces of touching spheres. When sphere are moved apart again, each one is left with half of the total original charge .