Question

An initially neutral conducting sphere is charged by induction. A second, identical, conducting sphere that is electrically neutral is brought into contact with the first then removed. When the two spheres are placed next to each other such that their centers are a distance 5 cm apart, they exert a force of 0.002 N on each other.

A. Determine the amount of charge that was placed on the first sphere by the induction process.

B. Determine the amount of charge on each sphere after they are brought into contact.

C. If an electron is placed between the two spheres a distance of 2.5 cm from the first (halfway between both), what bet force would be exerted on the electron?

D. If an electron is placed between the two spheres a distance of 2.0 cm from the first (3 cm from the second), what net force would be exerted on the electron?

Answer 1

(a)

let q be the charge by induction when the second, identical, conducting sphere that is electrically neutral is brought into contact with the first then removed the charge on the two bodies will be (q / 2) and (q / 2)

the force between them is F = 0.002 N with a seperation r = 5cm = 0.05 m

according to coulombs law we get

F = (1 / 4_o) (q₁q₂) / (r²)

here q₁ = q₂

= q / 2

solve for the amount of charge (q) that was placed on the first sphere by the induction process.

(b)

q / 2

(c)

electron charge q = 16 x 10^-20 C

the force will be equal and opposite the net force will be zero

(d)

this you can calculate from

F = (1 / 4_o) (q₁q₂) / (r²)

keeping r = 2 cm and r = 3 cm and find the net force