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
Answers
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. ]