Question

Two point charges, Q1=?37?C and Q2=49?C, are separated by a distance of 12 cm. The electric field at the point P is zero (Figure 1) .

How far from Q1 is P?

Answer 1

Electric field at any point (E) = field from Q1 + field from Q2

At P, E = 0 so..

E(Q1) + E(Q2) = 0

E = (K_e * q) / r^2

P must be closer to Q1, as |Q2|>|Q1|
so, let x be distance of P from Q1, so therefore (x+0.11m) is distance of p to Q2

i.e.
(K_e * -2.8*10^5) / x^2 + (K_e * 5.0*10^5) / (x+0.11)^2 = 0

then solve this equation for x;

you will get a nasty quadratic:
2.2*x^2 + 0.616*x + 0.03388 = 0

use quadratic formula to solve

gives;

x = -0.047 (i.e. 0.047m away, on the side of Q2)
or = 0.327 (i.e. 0.327m away, opposite side of Q1 to Q2)

you should also change this back into cm

4.7 or 32.7 cm