Question

Two point charges each experience a 1-N electrostatic force when they are 2 cm apart. If they are moved to a new separation of 8 cm, what is the magnitude of the electric force on each of them?
2 N

1/8 N

1/16 N

1/4 N

1/2 N

Answer 1

Electrostatic force between two points in space is defined as,

$F_e=\dfrac{Q_1Q_2}{4\pi r\epsilon_r\epsilon_0}$

The r is the distance between them.

So if,

$1N=\dfrac{Q_1Q_2}{4\pi 2cm\epsilon_r\epsilon_0}\Rightarrow 2\cdot1N=\dfrac{Q_1Q_2}{4\pi\cdot10^{-2}m\cdot\epsilon_r\epsilon_0}$

Than,

$\boxed{\dfrac{1}{4}N}=\dfrac{Q_1Q_2}{4\pi\cdot 8cm\cdot\epsilon_r\epsilon_0}\Rightarrow8\dfrac{1}{4}N\Leftrightarrow 2N=\dfrac{Q_1Q_2}{4\pi\cdot10^{-2}m\cdot\epsilon_r\epsilon_0}$

Hope this helps.

r3t40