Question

Determine the magnitude of electric field at point P due to two point charges both of charge +Q, with one point charge being at a distance R and the other being at a distance 2R :

• A. $\frac{3Q}{4\pi {ϵ}_0{R}^2}$
• B. $\frac{3Q}{16\pi {ϵ}_0{R}^2}$
• C. $\frac{2Q}{4\pi {ϵ}_0{R}^2}$
• D. $\frac{2Q}{16\pi {ϵ}_0{R}^2}$

Answer 1

The correct option is B $\frac{3Q}{16\pi {ϵ}_0{R}^2}$

Electric field at point P due to charge at distance $R$, $E_1=\frac{q}{4\pi {ϵ}_o{R}^2}$ (towards left)

Electric field at point P due to charge at distance $2R$, $E_2=\frac{q}{4\pi {ϵ}_o(2R{)}^2}=\frac{q}{16\pi {ϵ}_o{R}^2}$ (towards right)

Net electric field at p, $E_p=E_1-E_2=$ $\frac{q}{4\pi {ϵ}_o{R}^2}-$ $\frac{q}{16\pi {ϵ}_o{R}^2}=$ $\frac{3q}{16\pi {ϵ}_o{R}^2}$ (towards left)