Question

Two point charges A and B of charge +4 uc and-1 uc are placed in air at a distance1 m apart. The distance of the point from the charge B on the line
joining the charges, where the resultant electric field is zero, is ...
(A) 0.5 m (B) 1 m (C) 1.5 m (D) 2 m​

Answer 1

Given :

- Charge on A = + 4 uC

- Charge on B = - 1 uC

- Distance between them = 1 m

To find :

• The distance of the point from the charge B on the line joining the charges, where the resultant electric field is zero

Solution :

• Let a point P be on line joining charges at distance x m from charge B

• Enet = Electric field due to charge A, E1 + Electric field due to charge B, E2

E1 = k × (-1×10^-6) / x^2

E2 = k × 4×10^-6 / (1-x)^2

• Also, Enet = 0

E1 + E2 = 0

k × (-1×10^-6) / x^2 + k × 4×10^-6 / (1-x)^2 = 0

k × 4×10^-6 / (1-x)^2 = k × 1×10^-6 / x^2

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

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

3x^2 + 2x - 1 = 0

• x = 1/3 m from charge B