WBJEE · Physics · Magnetic Effects of Current
A thin charged rod is bent into the shape of a small circle of radius \(\mathrm{R}\) the charge per unit length of the rod being \(\lambda\). The circle is rotated about its axis with a time period \(T\) and it is found that the magnetic field at a distance ' \(d\) ' away \((d>>R)\) from the center and on the axis, varies as \(\frac{\mathrm{R}^{\mathrm{m}}}{\mathrm{d}^{\mathrm{n}}} .\) The values of \(\mathrm{m}\) and \(\mathrm{n}\) respectively are
- A \(m=2, n=2\)
- B \(m=2, n=3\)
- C \(m=3, n=2\)
- D \(m=3, n=3\)
Answer & Solution
Correct Answer
(D) \(m=3, n=3\)
Step-by-step Solution
Detailed explanation
\(\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \pi \mathrm{R}^{2} \mathrm{I}}{\left(\mathrm{R}^{2}+\mathrm{d}^{2}\right)^{3 / 2}} \quad \mathrm{I}=\frac{\mathrm{q}}{\mathrm{T}}\) \(=\frac{2 \pi \mathrm{R} \lambda}{\mathrm{T}}\)…
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