Question

Two tiny conducting spheres are identical and carry charges of -21.4 µC and +46.5 µC. They are separated by a distance of 2.39 cm.

(a) What is the magnitude of the force that each sphere experiences, and is the force attractive or repulsive?

(b) The spheres are brought into contact and then separated to a distance of 2.39 cm. Determine the magnitude of the force that each sphere now experiences, and state whether the force is attractive or repulsive.

Answer 1

here,

q1 = - 21.4 * 10^-6 C

q2 = 46.5 * 10^-6 C

r1 = 2.39 cm = 0.0239 m

a)

as the charges are of opposite sign

they will attract each other

magnitude of force , F = K * q1 * q2 /r^2

F = 9 * 10^9 * 21.4 * 10^-6 * 46.5 * 10^-6 /0.0239^2 N

F = 1.57 * 10^4 N

b)

when they are in contact

the charges are on same potential

as they are identical

the charge on each , Q = ( Q1 + Q2)/2

Q = ( - 21.4 uC + 46.5 uC) /2 = 12.55 uC

as they have the same charge

the force is repulsive

the magnitude of force , F = K * Q^2 /r^2

F = 9 * 10^9 * (12.55 * 10^-6)^2 /0.0239^2 N

F = 2.5 * 10^3 N