Question

Two identical charges q placed 2.0 mapart exert forces of magnitude 4.0 N on each other What is the value of the charge q? a) q 1.8 x 10- C b) q 2.1 x 10-5 C c) q 4.2 x

Answer 1

c)
`4.2*10^(-5)C`

Step-by-step explanation:

Coulomb's law says that the force exerted between two charges is inversely proportional to the square of distance between them, and is given by the expression:

`F=(kq_(1)q_(2))/(r^(2))`

where k is a proportionality constant with the value
`k=9*10^(9)(Nm^(2))/(C^(2))`

In this case
`q_(1)=q_(2)=q`, so we have:

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

Solving the equation for q, we have:

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

`q^(2)=(Fr^(2))/(k)`

`q=\sqrt{(Fr^(2))/(k)}`

Replacing the given values:

`q=\sqrt{(4.0N*(2.0m)^(2))/(9*10^(-9)(Nm^(2))/(C^(2)))}`

`q=4.2*10^(-5)C`