Magnetic Effects & Magnetism

JEE Main level, single correct, medium

86 of 276

Question 86 of 276

A Helmholtz coil has pair of loops, each with NN turns and radius RR. They are placed coaxially at distance RR and the same current II flows through the loops in the same direction. The magnitude of magnetic field at PP, midway between the centres AA and CC, is given by (Refer to figure):

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Answer: (B) 8Nμ0I53/2R\frac{8 N \mu_0 I}{5^{3 / 2} R}

Point PP is situated at the mid-point of the line joining the centres of the circular wires which have same radii (R). The magnetic fields (B⃗)(\vec{B}) at P\mathrm{P} due to the currents in the wires are in same direction.
Magnitude of magnetic field at point, PP
B=2{μ0NIR22(R2+R24)3/2}B=2\left\{\frac{\mu_0 N I R^2}{2\left(R^2+\frac{R^2}{4}\right)^{3 / 2}}\right\}
=μ0NIR253/28=8μ0NI53/2R=\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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