Question

2 point charges 4Q, Q are separated by 1m in air. At what point on the line joining the charges is the electric field intensity zero

Answer 1

let x be the point in line joining the charges x be the distance from 4Q charge
so At x el Electric field is zero then
K4Q/x²= KQ/(1-x)²
we get
4/x²= 1/(1-x)²
1-x= x/2
so 3x/2=1
x=2/3m
at X= 2/3 m Electric field will be zero

Answer 2

Let the point is be at a distance of xm.

Therefore at a point where Electric field intensity = 0

K(4Q)/x^2 = K(Q)/(1-x)^2

4(1-x)^2 = x^2

4(1+x^2-2x) = x^2

4+4x^2-8x = x^2

3x^2-8x+4 =0

3x^2-(6+2)x+4 =0

3x^2-6x-2x+4 =0

3x(x-2)-2(x-2) =0

(x-2)(3x-2) =0

x=2 or 2/3. (Ignoring x=2 since it is greater than actual distance between A and B).

Hence point is at a a distance of 2/3 from A .