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JEE Mains · Physics · STD 12 - 1. Electric charges and fields

Shown in the figure are two point charges \(+Q\) and \(-Q\) inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If \(\sigma _1\) is the surface charge on the inner surface and \(Q_1\) net charge on it and \(\sigma _2\) the surface charge on the outer surface and \(Q_2\) net charge on it then

  1. A \(\begin{array}{l}
    {\sigma _1}\, \ne \,0,\,\,{Q_1}\, = \,0\\
    {\sigma _2}\, = \,0,\,\,{Q_2}\, = \,0
    \end{array}\)
  2. B \(\begin{array}{l}
    {\sigma _1}\, \ne \,0,\,\,{Q_1}\, = \,0\\
    {\sigma _2}\, \ne \,0,\,\,{Q_2}\, = \,0
    \end{array}\)
  3. C \(\begin{array}{l}
    {\sigma _1}\, = \,0,\,\,{Q_1}\, = \,0\\
    {\sigma _2}\, = \,0,\,\,{Q_2}\, = \,0
    \end{array}\)
  4. D \(\begin{array}{l}
    {\sigma _1}\, \ne \,0,\,\,{Q_1}\, \ne \,0\\
    {\sigma _2}\, \ne \,0,\,\,{Q_2}\, \ne \,0
    \end{array}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\begin{array}{l}
{\sigma _1}\, = \,0,\,\,{Q_1}\, = \,0\\
{\sigma _2}\, = \,0,\,\,{Q_2}\, = \,0
\end{array}\)

Step-by-step Solution

Detailed explanation

Inside the cavity net charge is zero. \(\therefore \quad Q_{1}=0\) and \(\sigma_{1}=0\) There is no effect of point charges \(+Q\) \(Q\) and induced charge on inner surface on the outer surface. \(\therefore \quad Q_{2}=0\) and \(\sigma_{2}=0\)
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