Question

Two identically shaped conducting spheres, fixed in place, attract each other with a force of 1.296 N when separated by 50 cm. The spheres are connected by a thin wire and then the wire is removed. The speheres then repel each other with a force of 0.729 N. What were the initial charges of the spheres.

Answer 1

here,

let the charges be q1 and q2

r = 50 cm = 0.5 m

force between the charges , F = k * q1 * q2 /r^2

1.296 = 9 * 10^9 * q1 * q2 /0.5^2 .....(1)

and

when The spheres are connected by a thin wire and then the wire is removed ,

the are on same potential

as they are identical

the charge on spheres is same

so , q = (q1 - q2)/2

the force between charges = k * q^2 /r^2

0.729 = 9* 10^9 * ((q1 - q2)/2)^2 /0.5^2 ....(2)

from (1) and (2)

q1 = 3 * 10^-6 C and q2 = - 1.2 * 10^-5 C

or

q1 = - 3 * 10^-6 C and q2 = 1.2 * 10^-5 C