Two identical conducting small spheres are placed with their centers 0.220 m apart. One is given a charge of 12.0 nC and the other a charge of 16.0 nC. (a) Find the electric force exerted by one sphere on the other. magnitude N direction (b) The spheres are connected by a conducting wire. Find the electric force each exerts on the other after they have come to equilibrium. magnitude N direction

Explanation:

Force between two charges can be calculated with the help of following expression

F = kq₁q₂ / r² where F is force between charges  q₁ and q₂ and r is distance between the two. k is a constant .

F = 9 x 10⁹ x 12 x 10⁻⁹ x 16  x 10⁻⁹ / .22²

= 35702.47 x 10⁻⁹ N . The force will be directed away from the other charge ie it will be repulsive.

b) When the spheres are connected , charge will be equally distributed on them .

charge on each of them = (12 + 16) / 2 x 10⁻⁹

= 14 x 10⁻⁹ C

force = 9 x 10⁹ x (14 x 10⁻⁹)² / .22²

= 36446.28  x 10⁻⁹ N .

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west