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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Self Evaluation Test - Electrostatic Potential and Capacitance

  • question_answer
    Three concentric charged metallic spherical shells A, B and C have radii a, b and c; change densities \[\sigma ,-\sigma \] and \[\sigma \] and potentials \[{{V}_{A}},{{V}_{B}}\] and \[{{V}_{C}}\] respectively. Then which of the following relations is correct?

    A) \[{{V}_{A}}=\left( a+b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\]  

    B) \[{{V}_{B}}=\left( \frac{{{a}^{2}}}{b}-b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\]

    C) \[{{V}_{C}}=\left( \frac{{{a}^{2}}+{{b}^{2}}}{b}+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\]

    D) \[{{V}_{A}}={{V}_{B}}={{V}_{C}}=\left( a+b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\]

    Correct Answer: B

    Solution :

    [b] Potential due to a charged shell at an outside point \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{Q}{r}\] While that inside the shell\[=\frac{\sigma R}{{{\varepsilon }_{0}}}\], where R is the radius of the shell.


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