Two identical insulated metal spheres are separated d metres apart and carry charges of +q and...

Two identical insulated metal spheres are separated d metres apart and carry charges of +q and –q. The force that they exert on each other is 4 x 10-3 N. If the charged spheres are now separated by 3d metres, the magnitude of the new force between them is:

Solutions

Expert Solution

q = magnitude of charge on each sphere

r_i = distance between the two charges initially = d

F_i = force between the two charges initially = 4 x 10^-3 N

r_f = distance between the two charges finally = 3d

F_f = force between the two charges finally = ?

Using coulomb's law, we have

F_i = k q²/r_i² Eq-1

similarly, for final force, we have

F_f = k q²/r_f² Eq-2

Dividing Eq-2 by Eq-1

F_f /F_i = (k q²/r_f²) / (k q²/r_i²)

F_f /F_i = (q²/r_f²) (r_i²/q²)

F_f /F_i = r_i²/r_f²

F_f /(4 x 10^-3) = (d/(3d))²

F_f = (4 x 10^-3) /9

F_f = 4.44 x 10^-4 N

genius_generous answered 1 year ago

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