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)
JEE MAIN 2018, Diffcult
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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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