Question

Two charged objects exert an electrostatic force on each other and are 22 cm apart. By what factor would their force change if the the the distance was 44 cm apart?

Answer 1

We are asked to determine by what factor the electromagnetic force changes when the distance between the charges changes. To do that we will use the formula for the electromagnetic force. The force for the first distance is:

`F_1=k(q_1q_2)/(r_1^2)`

The force for the second distance is:

`F_2=k(q_1q_2)/(r_2^2)`

Now, we determine the quotient between the forces:

`(F_2)/(F_1)=(k(q_1q_2)/(r_2^2))/(k(q_1q_2)/(r_1^2))`

We can cancel out the value of "k" and the product of the charges:

`(F_2)/(F_1)=((1)/(r_2^2))/((1)/(r_1^2))`

Simplifying we get:

`(F_2)/(F_1)=(r_1^2)/(r_2^2)`

Now, we plug in the values:

`(F_2)/(F_1)=((22cm)^2)/((44cm)^2)`

Solving the operations:

`(F_2)/(F_1)=(1)/(4)`

Therefore, the second force is 1/4 of the first force.