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Question 38

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: In electrostatics, a conductor does not store any net charge inside.

Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.
Choose the correct answer from the options given below:

The assertion states: “A conductor has no net charge inside it.”

In electrostatic equilibrium, the electric field $$\mathbf{E}$$ inside a conductor is zero. By Gauss’s law, $$\oint \mathbf{E}\cdot d\mathbf{A}= \frac{Q_{\text{encl}}}{\varepsilon_0}$$. Since $$\mathbf{E}=0$$ everywhere on the Gaussian surface drawn wholly inside the conductor, the left side is zero, giving $$Q_{\text{encl}} = 0$$. Hence no net charge can reside in the interior; all excess charge moves to the outer surface. Therefore the Assertion (A) is true.

The reason says: “Inside a parallel plate capacitor (without dielectric), free charges experience a force and drift.” Between the plates of an isolated parallel-plate capacitor there exists a uniform electric field $$\mathbf{E} = \frac{\sigma}{\varepsilon_0}$$ (directed from positive to negative plate). Any free charge placed in this region will indeed feel the force $$\mathbf{F}=q\mathbf{E}$$ and will drift toward one of the plates. Hence the Reason (R) is also true.

However, the phenomenon of charge drift inside the gap of a capacitor explains the behaviour of charges in a region where a finite electric field already exists; it does not account for the absence of net charge inside a conductor, which follows from zero electric field and Gauss’s law as shown above. Thus R is not the correct explanation of A.

Both A and R are true, but R is NOT the correct explanation of A. Hence the correct choice is:

Option B which is: Both A and R are true, but R is NOT the correct explanation of A

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