Q3.15 Zero net field (K)
Two particles are fixed to a horizontal axis, one of charge +q at +2 cm from the origin, the other of charge -4q at +7 cm from the origin.
At what coordinate on the axis is the field produced by them equal to zero?
Hint
Reveal

Hint
The field will be zero where the electrostatic forces on a test positive charge are equal and opposite.Solution
Reveal

Solution
Let’s identify the fixed charges as q1 has charge +q, x=2cm and q2 has charge -4q at x=7cm.
We imagine at test positive charge at x=L; the repulsive force between it and q1 is given by

and the attractive force between the test charge and q2 is

Equating these gives:

You can just take square roots here, as in Q3.13
or if you prefer, expand and factorise:
So L = -3cm or
The value where the Electric field is zero is given by L=-3cm. (Think about why the other root cannot be correct)
(Note you can check your working for this using the Java applet in S2.12 )