Question

Deduce an expression for the electric field at a
point due to a system of N point charges.
system of point charges​

Answer 1

Answer:

Answer: The 'electric potential' due to a point charge is kq/r. Solution: Let us consider q' be the point charge placed at a distance r from the charge q.

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Answer 2

The electric field is the space around a charged particle or object within which a force would be exerted on other charged particles or objects.

Electric field intensity due to a system of N point charges is given below.

Let us consider a system of N charge q₁, q₂, till qN having position vectors r₁, r₂, till rN with respect to origin 0.  The electric field at point P whose position vector is r.

According to Coulomb's law, the force on charge q₀ due to charge q₁ is

F₁ = 1/4πε₀r₁²×q₀×q₁  

Hence the electric field at point P due to charge q₁   is

E₁ = F₁/q₀  

Similarly, electric field at P due to charge q₂ is E₂ = 1/4πε₀r₂²×q₀q₁ / q₀    

According to the principle of supervision of electric charge, the electric field at any point due to a group of point charges is equal to the vector sum of the electric fields produced by each charge individually at that point, when all other charges are assumed to be absent.

Hence, the electric field at point P due to the system of N charges is

E  = E₁+E₂+E3+....+Eₙ

 = I/4πε₀ [q₁/r₁² + q₂/r₂² +....+ qₙ/rₙ²]

 = 1/4πε₀∑qₙ/rₙ²

Therefore, the electric field at a point due to system of N point charges is 1/4πε⁰∑qₙ/rₙ²

 

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