Question

Two positive point charges q_1=16muC and q_2=4muC are separated in vacuum by a distance of 3.0m. Find the point on the line between the charges where the net electric field is zero.-

Answer 1

The point on the line between the charges where the net electric field is zero can be calculated by force balance:

Please see the attachment for the solution.

Answer 2

Given:

Charge  $q_1=16 \mu C$

            $q_2=4\mu C$

Distance $= 3m$

To find: The point on the line between the charges where the net electric field is zero.

Solution:

Between the charges the two field contributions have opposite directions, and the net electric field is zero at a point ( P) where the magnitude of $E_1$ and $E_2$ are equal.

However, since $q_2<q_1$ point P must be closer to $q_2$ in order that the field of the smaller charge can balance the field of the larger charge.

At point P,        $E_1=E_2$

                       $\frac{kq_1}{r_1^2} = \frac{kq_2}{r_2^2}$

                    $(\frac{r_1}{r_2})^2 = \frac{q_1}{q_2}$

                    $\frac{16}{4} = (\frac{r_1}{r_2})^2$

                     $\frac{r_1}{r_2} = 2$

                  $r_1 = 2r_2 .........(i)$

Also given

               $r_1+r_2=3.0m ......(ii)$

Solving both equations

we get ,

               $r_1=2m$

or            $r_2=1m$

Thus, the point P is at a distance of $2 m$ from $q_1$ and $1m$ from $q_2$.