NEET · Physics · STD 12 - 1. Electric charges and fields

A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance r from the centre

A increases as \(\mathrm{r}\) increases for \(\mathrm{r}<\mathrm{R}\) and for \(\mathrm{r}>\mathrm{R}\)
B zero as \(\mathrm{r}\) increases for \(\mathrm{r}<\mathrm{R}\), decreases as \(\mathrm{r}\) increases for \(\mathrm{r}>\mathrm{R}\)
C zero as \(\mathrm{r}\) increases for \(\mathrm{r}<\mathrm{R},\) increases as \(\mathrm{r}\) increases for \(\mathrm{r}>\mathrm{R}\)
D decreases as \(\mathrm{r}\) increases for \(\mathrm{r}<\mathrm{R}\) and for \(\mathrm{r}>\mathrm{R}\)

Verified Solution

Answer & Solution

Correct Answer

(B) zero as \(\mathrm{r}\) increases for \(\mathrm{r}<\mathrm{R}\), decreases as \(\mathrm{r}\) increases for \(\mathrm{r}>\mathrm{R}\)

Step-by-step Solution

Detailed explanation

For a metal sphere \(\mathrm{E}_{\mathrm{m}}=0\) and \(\overline{\mathrm{E}}_{\infty}=\frac{\mathrm{Kq}}{\mathrm{r}^{2} \mathrm{f}}\)

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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