Question

the electric field at origin due to infinite number of charges on x axis are 1, 2, 4, 8,​

Answer 1

Answer:

Explanation:

Here q₁ + q₂ + q₃ + q₄ ... = q

and r₁ = 1 , r₂ = 2 , r₃ = 4 , r₄ = 8...

Hence,

E = 1/4 ∏ ε { (q/12) + (q/22) + (q/42) + .......}

E = 1/4 ∏ ε .q { (1/12) + (1/22) + (1/42) + .......}

E = 1/4 ∏ ε .q. S∞ (S infinity)

where, S (infinity) = a/1-r = 1/1-(1/4) = 4/3

Hence,

E= q/3 ∏ ε