Question

Two point charges, Q1=−36μC and Q2=49μC, are separated by a distance of 12 cm. The electric field at the point P is zero.

How far from Q1 is P?

Answer 1

Suppose at distance d from charge -36 C net electric field is zero, then

Electric field is given by:

E = kQ/R^2

Since we know that direction of electric field due to +ve charge will be away from charge and due to -ve charge will be towards the charge. In given case since Q1 is -ve and Q2 is +ve, So electric field will be zero towards the left side of Q1 (Since |Q1| < |Q2|)

Enet = E1 - E2 = 0

E1 = E2

kQ1/r1^2 = kQ2/r2^2

Q1 = -36 C

Q2 = 49 C

r1 = distance between point P and Q1 = d

r2 = distance between point P and Q2 = d + 0.12 (Since distance between Q1 and Q2 is 12 cm (0.12 m), and P is on the left side of Q1)

Using above values:

Q1/r1^2 = Q2/r2^2

36/d^2 = 49/(d + 0.12)^2

(d + 0.12)/d = sqrt (49/36) = 7/6

6*(d + 0.12) = 7*d

6d + 6*0.12 = 7d

d = 6*0.12 = 0.72 m = 72 cm

So electric field will be zero at 72 cm left of charge Q1

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