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