Question

A negative charge of -0.590 μc exerts an upward 0.600-n force on an unknown charge that is located 0.300 m directly below the first charge. what is the value of the unknown charge (magnitude and sign)?

Answer 1

To calculate the value of unknown charge, we use the formula the electric force between two charges

$F=\frac{1}{4\pi \epsilon_{0}  }\frac{Qq}{r^2}$

Here, q is unknown charge ,  $Q=-0.590 \mu C$,  $r=0.300 N$ and $\frac{1}{4\pi \epsilon_{0}  } = k= 8.988 \times 10^9 Nm^2/C^2$

Now substituting the given values in above formula we get

$0.600 N=  8.988 \times 10^9 Nm^2/C^2 ( \frac{-0.590 \mu C \times q}{(0.300)^2}$

or

$q = 10.1 \mu C$

The unknown charge is positive because the force between charges is attractive.