Question

Two similar spheres when placed 2 cm apart attract each other with a.
force of 4 dynes. The spheres are connected by a wire. On removing
the wire the spheres now repel each other with a force of 2.25 dynes.
Calculate the initial charges on the sphere

Answer 1

Given,

Two similar spheres when placed 2 cm apart attract each other with a force of 4 dynes. The spheres are connected by a wire. On removing

the wire the spheres now repel each other with a force of 2.25 dynes.

To find,

initial charges on the sphere.

let Q and -q are charge on spheres respectively.

initially, force between them F = kqQ/r² [attractive force ]

⇒4 Dyne = kqQ/(2cm)²

⇒4 = qQ/4 [ in CGS , k = 1 ]

⇒qQ = 16 ........(1)

The spheres are connected by a wire. so, charge on each sphere , q' = (Q - q)/2

so, force between them, F' = kq'²/r²

⇒2.25 Dyne = k{(Q - q)/2}²/(2cm)²

⇒2.25 = (Q - q)²/(4 × 4)

⇒(Q - q)² = 36 = (6)²

⇒Q - q = 6 .........(2)

from equation (1) we get,

⇒Q - 16/Q = 6

⇒Q² - 6Q - 16 = 0

⇒Q² - 8Q + 2Q - 16 = 0

⇒Q = 8, -2

then, q = -2, 8

therefore charges on the sphere are 8 statecoulomb and -2 statecoulomb respectively.

[ note : if answer is given in coulomb, just change statecoulomb to coulomb. ]