SATHEE: Electrostatics Question 787

Electrostatics Question 787

Question: Two concentric conducting spherical shells of radii $a_{1}$ and $a_{2}$

$(a_{2} > a_{1})$ are charged to potentials $ϕ_{1}$ and $ϕ_{2}$ , respectively. Find the charge on the inner shell.

Options:

A) $q_{1} = 4 π ε_{0} (\frac{ϕ_{1} - ϕ_{2}}{a_{2} - a_{1}}) a_{1} a_{2}$

B) $q_{1} = 4 π ε_{0} (\frac{ϕ_{1} + ϕ_{2}}{a_{2} + a_{1}}) a_{1} a_{2}$

C) $q_{1} = 4 π ε_{0} (\frac{ϕ_{1} - ϕ_{2}}{a_{2} + a_{1}}) a_{1} a_{2}$

D) $q_{1} = 4 π ε_{0} (\frac{ϕ_{1} + ϕ_{2}}{a_{2} - a_{1}}) a_{1} a_{2}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ϕ_{1} = \frac{k q_{1}}{a_{1}} + \frac{k q_{2}}{a_{2}}$

$ϕ_{2} = \frac{k q_{1}}{a_{2}} + \frac{k q_{2}}{a_{2}}$ Solve to get $q_{1} = 4 π ε_{0} [\frac{ϕ_{1} - ϕ_{2}}{a_{2} - a_{1}}] a_{1} a_{2}$

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Electrostatics Question 787

Question: Two concentric conducting spherical shells of radii a1 and a2

Options:

Answer:

Solution:

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Question: Two concentric conducting spherical shells of radii $a_{1}$ and $a_{2}$