COMEDK · Physics · 17. Electrostatics

A charge \(q\) is enclosed by an imaginary Gaussian surface.

If the radius of Gaussian surface is increasing at a rate \(\frac{d r}{d t}=\alpha\), then flux linked with surface is

A increasing at a rate, \(\frac{d \phi}{d t}=\alpha\)
B decreasing at a rate, \(\frac{d \phi}{d t}=-\alpha\)
C decreasing at a rate, \(\frac{d \phi}{d t}=\frac{1}{k}\)
D \(\frac{q}{\varepsilon_0}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{q}{\varepsilon_0}\)

Step-by-step Solution

Detailed explanation

Electric flux coming out from a surface does not depend on its surface area. It depends only on charge enclosed by surface. As, flux, \(\quad \phi=\frac{q}{\varepsilon_0}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A charge \(q\) is enclosed by an imaginary Gaussian surface.If the radius of Gaussian surface is increasing at a rate \(\frac{d r}{d t}=\alpha\), then flux linked with surface is

Step-by-step Solution

A charge \(q\) is enclosed by an imaginary Gaussian surface.

If the radius of Gaussian surface is increasing at a rate \(\frac{d r}{d t}=\alpha\), then flux linked with surface is