WBJEE · Physics · Magnetic Effects of Current
As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius 'r' concentrically inside a square of side ' \(a\) ', where \(a: r=8: \pi\). A battery B drives a current through the wire. If the battery B and the gap G are of negligible sizes, determine the strength of magnetic field at the common centre \(O\).
- A \(\cdot \frac{\mu_{0} \mid}{2 \pi a} \sqrt{2}(\sqrt{2}-1)\)
- B \(\frac{\mu_{0} I}{2 \pi a}(\sqrt{2}+1)\)
- C \(\frac{\mu_{0} I}{\pi a} 2 \sqrt{2}(\sqrt{2}+1)\)
- D \(\frac{\mu_{0} I}{\pi \mathrm{a}} 2 \sqrt{2}(\sqrt{2}-1)\)
Answer & Solution
Correct Answer
(D) \(\frac{\mu_{0} I}{\pi \mathrm{a}} 2 \sqrt{2}(\sqrt{2}-1)\)
Step-by-step Solution
Detailed explanation
Hint: \(\frac{a}{r}=\frac{8}{\pi}, r=\frac{\pi a}{8}\) \(B=\frac{\mu_{0} \mid}{2 r}-\frac{4 \mu_{0} I}{4 \pi a / 2} \times \sqrt{2}=\frac{\mu_{0} I}{2 r}-\frac{2 \sqrt{2} \mu_{0} I}{\pi a}=\frac{\mu_{0} \mid \times 8}{2 \pi a}-\frac{2 \sqrt{2} \mu_{0} I}{\pi a}\)…
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