AP EAMCET · PHYSICS · Magnetic Effects of Current

When a helium nucleus covers a circle of radius \(0.8 \mathrm{~m}\) in \(2 \mathrm{~s}\), find the value of magnetic field \(B\) at the centre of the circle.

A \(\frac{10^{-19}}{\mu_0} \mathrm{~T}\)
B \(\mu_0 \times 10^{-19} \mathrm{~T}\)
C \(2 \mu_0 \times 10^{-19} \mathrm{~T}\)
D \(\frac{2 \times 10^{-19}}{\mu_0} \mathrm{~T}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mu_0 \times 10^{-19} \mathrm{~T}\)

Step-by-step Solution

Detailed explanation

Charge on helium nucleus, \(q=+2 e=2 \times 1.6 \times 10^{-19} \mathrm{C}=3.2 \times 10^{-19} \mathrm{C}\) Radius of helium nucleus, \(r=0.8 \mathrm{~m}\) Time period, \(T=2 \mathrm{~s}\) \(\therefore\) Current associated with helium nucleus,…

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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