Question

A +4μC charge is at x=0 and a -2μC charge is at x=10cm. At what point along the x-axis (in m) is the electric field zero?

Answer 1

Suppose at distance 'd' from charge +4 μC 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 right side of Q2 (Since |Q1| > |Q2|)

Enet = E1 - E2 = 0

E1 = E2

kQ1/r1^2 = kQ2/r2^2

Q1 = +4 μC

Q2 = -2 μC

r1 = distance of point from Q1 = d

r2 = distance of point from Q2 = d - 0.10

Using above values:

Q1/r1^2 = Q2/r2^2

4/d^2 = 2/(d - 0.10)^2

(d - 0.10)/d = sqrt (2/4) = 0.707

d - 0.10 = 0.707*d

d = 0.10/(1 - 0.707)

d = 0.3413 m = 34.13 cm

So electric field will be zero at x = 34 cm

"Let me know if you have any query."