JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2018
- Hard
- MCQ
A Helmholtz coil has pair of loops, each with \(N\) turns and radius \(R\). They are placed coaxially at distance \(R\) and the same current \(I\) flows through the loops in the same direction. The magnitude of magnetic field at \(P\), midway between the centres \(A\) and \(C\), is given by (Refer to figure)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\frac{{8N{\mu _0}I}}{{{5^{3/2}}R}}\)
Step-by-step Solution
Detailed explanation
Point \(P\) is situated at the mid-point of the line joining the centres of the circular wires which have same radii \((R)\). The magnetic fields \((\vec{B})\) at \(P\) due to the currents in the wires are in same direction.
Magnitude of magnetic fieldat point, \(P\)
\(B = 2\left\{ {\frac{{{\mu _0}NI{R^2}}}{{2{{\left( {{R^2} + \frac{{{R^2}}}{4}} \right)}^{3/2}}}}} \right\}\)
\(=\frac{\mu_{0} N I R^{2}}{\frac{5^{3 / 2}}{8}}=\frac{8 \mu_{0} N I}{5^{3 / 2} R}\)
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