Question

Deduce the expression for the electric field E due to a system of two charges q1 and q2 with position vectors r1 and r2 at a point r with respect to common origin

Answer 1

Let V₁ and V₂ be the electric potentials of the field E at the point having position vectors are r₁ and r₂ ( as shown in figure)
Now, work done in bringing q₁ from infinity to r₁ against the external field is given by W₁ = q₁V₁
Similarly Workdone in bringing q₂ from infinity to r₂ against the external fiedl is given by W₂ = q₂V₂

Also here, q₁ is exerted the force on q₂.
So, Workdone on q₂ against the force exerted by q₁ = U₁₂ = Kq₁q₂/|r₁₂|
r₁₂ is the separation between q₁ and q₂

Hence, Workdone in assembling two charges W = W₁ + W₂ + U₁₂
So, W = q₁V₁ + q₂v₂ + Kq₁q₂/|r₁₂|

Answer 2

Answer:

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Explanation:

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