Question

A small plastic sphere with a charge of -5nC is near another plastic sphere with a charge of -12nC. (a) If the spheres repel one another with a force of magnitude 8.2 x 10^-4, what is the distance between the spheres? (b) What is the new value of the force if the distance doubles its original value?

Answer 1

(a) given that :

charge on plastic sphere, q₁ = -5 x 10^-9 C

charge on another plastic sphere, q₂ = -12 x 10^-9 C

magnitude of force, F = 8.2 x 10^-4

According to coulomb's law,

F = k q₁ q₂ / r₁²                                     { eq.1 }

where, k = 9 x 10⁹ Nm²/C²

inserting the values in above eq.

(8.2 x 10^-4) = (9 x 10⁹ Nm²/C²) (-5 x 10^-9 C) (-12 x 10^-9 C) / r₁²  

r₁² = (540 x 10^-9 Nm²) / (8.2 x 10^-4)

r₁ = 65.85 x 10^-5

r = 0.0256 m

(b) the new value of the force if the distance doubles its original value which is given as ::

F_new = k q₁ q₂ / r₂²                                     { eq.2 }

where, r₂ = 2 r₁

inserting the value of 'r₂' in eq.2,

F_new = k q₁ q₂ / (2 r₁)²

F_new = k q₁ q₂ / 4 r₁²   

F_new = (F/ 4)                                               { from eq.1 }

inserting the value of 'F' in above eq.

F_new = (8.2 x 10^-4 N) / 4

F_new = 2.05 x 10^-4 N