Question

two tiny spheres, A and B, or mass 5g each each carry equal positive charge 2.0uC. They are connected by a .5m long insulating string with negligible mass. only electric forces are relevant in this problem. A) what is the tension in the string B)what is the electric potential energy of the problem c) if the string is cut what is the speed of sphere A when the two are very far apart

Answer 1

a) since the spheres have same Positive charge on them , they repul each other due to Electric force of repulsion.

This Electric force of repulsion creates tension in the string connecting the two spheres.

so Tension = Electric force of repulsion

Electric force of repulsion is given as

k = 9 x 10^9 Nm²/C²   ,   Q1 = Q2 =charge on each sphere = 2 x 10^-6 C (given)   

r = distance between the spheres = 0.5 m (given)

So Tension force = T = F = 0.144 N

b) the electric Potential energy is given as :

inserting the values we get

E = 0.072 J

c) When the string is cut , the spheres move away from each other and hence the Potential energy of sytem converts to kinetic energy.

so Kinetic energy of two spheres = Electric Potential energy

Kinetic energy is given as , KE = (0.5) m V²   , m = mass= 0.005 kg , V = speed = ?

KE of A + KE of B = E

(0.5) m V² + (0.5) m V² = 0.072 J

m V² = 0.072

V² = 0.072 / 0.005

V = 3.79 m/s