Assertion and Reason on Net Charge inside Conductor and Capacitor

To determine the correct option, let us analyze Assertion A and Reason R individually:

1. Analysis of Assertion A:

   • In electrostatic equilibrium, the electric field inside the bulk volume of a conductor is strictly zero ($\vec{E} = 0$).
   • According to Gauss's Law, the total electric flux through any closed Gaussian surface drawn entirely inside the conductor is given by: $\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0}$
   • Since $\vec{E} = 0$ everywhere inside the bulk conductor, the net enclosed charge inside any internal Gaussian surface must be zero ($q_{\text{enclosed}} = 0$).
   • This implies that the volume charge density inside the conductor is zero ($\rho = 0$), and any net excess charge resides entirely on the outer surface of the conductor.
   • Thus, Assertion A is true.

2. Analysis of Reason R:

   • Between the plates of a charged capacitor (with no dielectric medium), a uniform electric field $\vec{E}$ exists pointing from the positively charged plate to the negatively charged plate.
   • If a free charge carrier carrying charge $q$ is introduced into the region between the plates, it experiences an electrostatic force: $\vec{F} = q\vec{E}$
   • This force causes the charge carrier to accelerate and drift toward the oppositely charged plate.
   • Thus, Reason R is true.

3. Conclusion:

   • Assertion A is explained by Gauss's Law and the property of electrostatic equilibrium in conductors, which forces internal electric fields and net internal volume charges to be zero.
   • Reason R describes the effect of the electric field between capacitor plates on a free charge carrier, which is a correct statement but is logically unrelated to why a bulk conductor cannot hold net charge inside its volume.

Therefore, Both A and R are true but R is NOT the correct explanation of A.

Correct Option: B