Two point charges q₁ and q₂ lie on a circle of unit radius. The electric field at the centre is $\vec{E}$ . If $\vec{r_1}$ is the position vector of the centre with respect to q₁, find $\vec{r_2}$ , the position vector of the centre with respect to q₂.
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Question

Two point charges q₁ and q₂ lie on a circle of unit radius. The electric field at the centre is E ⃗ \vec{E} E . If r 1 ⃗ \vec{r_1} r 1 is the position vector of the centre with respect to q₁, find r 2 ⃗ \vec{r_2} r 2 , the position vector of the centre with respect to q₂.

Physics · Electrostatic

G1 Physics · Accepted Answer

Step 1: Because the circle radius is 1, the field at the centre due to q₁ is kq₁𝐫₁ and due to q₂ is kq₂𝐫₂. Step 2: Superposition gives 𝐄=kq₁𝐫₁+kq₂𝐫₂. Step 3: Rearranging, 𝐫₂=(𝐄-kq₁𝐫₁)/(kq₂). Final: D.