Three concentric, thin, spherical, metallic shells have radii 1 cm, 2 cm and 4 cm and they are held at
potentials 10 V, 0 V and 40 V respectively. Taking the origin at the common centre, calculate the
potential (in V) at r = 1.25 cm.

Question

Three concentric, thin, spherical, metallic shells have radii 1 cm, 2 cm and 4 cm and they are held at

potentials 10 V, 0 V and 40 V respectively. Taking the origin at the common centre, calculate the

potential (in V) at r = 1.25 cm.

TestHub · Accepted Answer

k q₁ / 1 + k q₂ / 2 + k q₄ / 4 = 10 (1)

2 k q₁ / 1 + k q₂ / 2 + k q₃ / 1 = 0 (2)

4 k q₁ / 1 + 4 k q₂ / 2 + 4 k q₃ / 1 = 40 (3)

(1) - (2) ⇒ 2 k q₁ = 10

At r = 1.25 cm,

V = (1 / 1.25) × (k q₁ / 2 + k q₂ / 4 + k q₃) = (1 / 1.25) × (20 + (10 - 20)) = 6 V

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