JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2019
- Hard
- MCQ
An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. the radius of the loop is \(a\) and distance of its centre from the wire is \(d (d >> a)\). If the loop applies a force \(F\) on the wire then
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(F \propto {\left( {\frac{a}{d}} \right)^2}\)
Step-by-step Solution
Detailed explanation
Force on one pole
\(F = \frac{{m{\mu _0}I}}{{2\pi \sqrt {{d^2} + {x^2}} }}\)
\(m=\) pole strength
Total force \(=2 F \sin \theta\)
\(=\frac{2 \times \mu_{0} \operatorname{Im} \times x}{2 \pi \sqrt{d^{2}+a^{2}} \sqrt{d^{2}+a^{2}}}=\frac{\mu_{0} \operatorname{Im} x}{\pi\left[d^{2}+a^{2}\right]}\)
\(=m 2 x=M=I \pi a^{2}\)
Total force \(=\frac{\mu_{0} I a^{2}}{2\left(d^{2}+a^{2}\right)}\)
\(\approx \frac{\mu_{0} I a^{2}}{2 d^{2}} \quad[\because d>>a]\)
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