Find the amount of work done in shifting a unit positive charge from A to B in the above case (two uniformly charged spherical rings of same radii )
Answers
Answer:
workdone =9×10^9×Q^2 joule
we have to find the work done in shifting a unit positive charge from A to B in the above case.
solution : workdone is product of charge and potential difference.
let's first find potential difference.
potential at A,
V₁ = potential due to ring of centre A + potential due to due to centre B at A
= kq/R - kq/√(R² + d²)
similarly, potential at B,
V₂ = potential due to ring of centre B + potential due to ring of centre B at A.
= -kq/R + kq/√(R² + d²)
potential difference, ∆V = V₁ - V₂
= kq/R - kq/√(R² + d²) - [-kq/R + kq/√(R² + d²)]
= 2kq/R - 2kq/√(R² + d²)
now Workdone to move a unit charge from A to B, W = q∆V
= q[2kq/R - 2kq/√(R² + d²) ]
= 2kq²/R - 2kq²/√(R² + d²)]
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