Two identical conducting small spheres are placed with their centers 0.395 m apart. one is given a charge of -12.0 nc and the other a charge of -15.0 nc.
(a) find the electric force exerted by one sphere on the other.(magnitude)
(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)

Answer :

(a). The magnitude of the electric force exerted by one sphere on the other is

(b). The  electric force each exerts on the other after they have come to equilibrium is

Explanation:

Given that,

Distance = 0.395 m

Charge of first sphere = -12.0 nC

Charge of second sphere = -15.0 nC

(a). We need to calculate the magnitude of the electric force exerted by one sphere on the other

Using formula of electric force

Where,

r = distance

Put the value into the formula

(b). The identical spheres are connected by a conducting wire.

Both charges are same so the force is repulsive.

We need to calculate the net charge

Using formula of charge

Put the value into the formula

We need to calculate the magnitude of the electric force each exerts on the other after they have come to equilibrium

Using formula of electric force

Put the value into the formula

Hence, (a). The magnitude of the electric force exerted by one sphere on the other is

(b). The electric force each exerts on the other after they have come to equilibrium is

495.05 m

Explanation:

Given:

Initial velocity of the bullet, u = 1000 m/s, mass of the bullet, m = 10 g, mass of the wooden block, M = 1000 g,

From the swinging of the wooden block just after the collision with the bullet to its maximum height, using conservation law of mechanical energy we have that,

1/2(m+M) = (m+M)gh

Where h = the vertical height of the block in the direction will the block swing, and g = acceleration due to gravity = 10

=> v=

Using the conservation law of linear momentum,

mu = (m+M)v

mu = (m+M) (where v=)

=>h = *

h=