TS EAMCET · Physics · Magnetic Effects of Current

A dielectric circular disc of radíus \(R\) carries a unform surface charge density \(\sigma\). If it rotates about its axis with angular velocity \(\omega\), the magnetic fíeld at the cente of dísc is :

A \(\frac{\mu_0 \sigma \omega R^2}{2 \pi}\)
B \(\frac{\mu_0 \sigma \omega R}{2}\)
C \(\frac{\mu_0 \sigma \omega R^2}{4}\)
D \(\frac{\mu_0 \sigma \omega R^2}{2 \sqrt{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\mu_0 \sigma \omega R}{2}\)

Step-by-step Solution

Detailed explanation

Let us assumed a ring like element of the disc of radius \(r\) and thickness \(d r\). If \(\sigma\) is the surface charge density, then the charge on the element. \( d q=\sigma(2 \pi r) d r \) Current \(d i\) associated with rotating charge \(d q\) is…

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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