SATHEE: Electrostatics Question 231

Electrostatics Question 231

Question: If on the concentric hollow spheres of radii $r$ and $R (> r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is [IIT 1981; MP PMT 2003]

Options:

A) $\frac{Q (R^{2} + r^{2})}{4 π ε_{0} (R + r)}$

B) $\frac{Q R}{R + r}$

C) Zero

D) $\frac{Q (R + r)}{4 π ε_{0} (R^{2} + r^{2})}$

Show Answer

Answer:

Correct Answer: D

Solution:

$q_{1} + q_{2} = Q$

and $\frac{q_{1}}{4 π r^{2}} = \frac{q_{2}}{4 π R^{2}}$ (given) $q_{1} = \frac{Q r^{2}}{R^{2} + r^{2}}$

and $q_{2} = \frac{Q R^{2}}{R^{2} + r^{2}}$

Potential at common centre $\frac{1}{4 π ε_{0}} [\frac{Q r^{2}}{(R^{2} + r^{2}) r} + \frac{Q R^{2}}{(R^{2} + r^{2}) R}] = \frac{Q (R + r)}{4 π ε_{0} (R^{2} + r^{2})}$

Electrostatics Question 231

Question: If on the concentric hollow spheres of radii $r$ and $R (> r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is [IIT 1981; MP PMT 2003]

Options:

Answer:

Solution:

Engineering Preparation

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NCERT Books & Solutions

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Syllabus

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Sample Mock Test

Mentorship

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Electrostatics Question 231

Question: If on the concentric hollow spheres of radii r and R(>r) the charge Q is distributed such that their surface densities are same then the potential at their common centre is [IIT 1981; MP PMT 2003]

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: If on the concentric hollow spheres of radii $r$ and $R (> r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is [IIT 1981; MP PMT 2003]