Question

Three charges each of value Q are placed at points A(-k,0),O(0,0) & B(0,k). If force on point charge at A is ai(cap)+ bj(cap) then force on point charge at B is.​

Answer 1

Given info : Three charge each of value Q are placed at points A(-k, 0) , O(0, 0) and B(0, k). the force on the point charge at A is a i + b j.

To find : the force on the point charge at B is...

solution : at point A,

electric force due to O = Q²/4πε₀k² (-i)

electric force due to B = Q²/4πε₀(√(2k)²) (-i - j)/√2

let Q²/4πε₀k² = F

so, electric force at A = F(-i) + F/2√2 (-i - j)

= (-F - F/2√2)i + (-F/2√2)j

so, a = -F - F/2√2 ...(1)

and b = -F/2√2 ....(2)

now, at point B,

electric force due to O = Q²/4πε₀k² (j)

electric force due to A = Q²/4πε₀(√(2k)²)(i + j)/√2

so electric force at B = F j + F/2√2 (i + j)

= (F + F/2√2)j + (F/2√2) i

from equations (1) and (2) we get,

Electric force at B = -aj - bi = -b i - a j

Therefore the electric force at point B is -b i - a j