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Two thin metallic spherical shells are placed concentrically with radii R1 and R2, where R1 > R2. If the shells carry charges Q1 and Q2 respectively, what is the electric potential at a point located at distance r such that R2 < r < R1? (Take k = 1/(4πϵ0))

1. k(Q1 + Q2)/r
2. k(Q1/r + Q2/R2)
3. k(Q2/r + Q1/R1)
4. k(Q1/R1 + Q2/R2)

Correct answer: k(Q2/r + Q1/R1)

Solution

At R2 < r < R1 the point is outside the inner shell (Q2 contributes kQ2/r) and inside the outer shell (Q1 contributes the constant kQ1/R1). So V = k(Q2/r + Q1/R1).

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