Question

1. The force between a pair of charges is 100 newtons. The distance between the charges is 0.01 meter. If one of the charges is 2 u 10-10 C, what is the strength of the other charge?

2. The force between two charges is 2 newtons. The distance between the charges is 2 u 10-4 m. If one of the charges is 3 u 10-6 C, what is the strength of the other charge?

Answer 1

(1)
`4.4835*10^(17)C`

(2)
`2.9748*10^(-12)C`

Step-by-step explanation:

Force Between two charges is give by.

`F=k(Q_1 *Q_2)/(r^2)` , here k is called coulomb constant and has value =
`8.967*10^9Nm^2/C`.

(1) case, F =100N, r = 0.1m and
`Q_1`=
`2*10^(-10)C` substituting these values in above equation and solving for unknown gives us.

`Q_2 = 4.4835*10^(17)C`.

(2) Case, F = 2N, r =
`2*10^(-4)m` and
`Q_1=3*10^(-6)C`.

again by substituting these in above equation and solving for unknown gives us.

`Q_2=2.9748*10^(-12)C.`

Answer 2

1.
`Q = 5.56 * 10^(-3) C`

2.
`Q = 2.97 * 10^(-12) C`

Step-by-step explanation:

1. Electrostatic force is given as:

`F = (kqQ)/(r^2)`

where k = Coulombs constant

q = charge of first charge

Q = charge of the second charge

r = distance between them

From the question:

F = 100 N

q =
`2 * 10^(-10) C`

r = 0.01 m

We need to find Q.

From the formula of force, we have that Q is:

`Q = (Fr^2)/(kq)`

`Q = (100 * 0.01^2)/(8.99 * 10^9 *2 * 10^(-10)) \\\\\\Q = (0.01)/(1.798)\\ \\\\Q = 0.00556 C = 5.56 * 10^(-3) C`

This is the charge, Q, of the second charge.

2. From the question:

F = 2 N

q =
`3 * 10^(-6) C`

r =
`2 *10^(-4) m`

We need to find Q.

Using the same formula for Q as in 1. above, we have that:

`Q = (2 * (2 *10^(-4))^2)/(8.99 * 10^9 *3 * 10^(-6)) \\\\\\Q = (8 * 10^(-8))/(26970)\\ \\\\Q = 2.97 * 10^(-12) C`

This is the charge, Q, of the second charge.