Magnetic Effects & Magnetism

JEE Main level, single correct, medium

85 of 276

Question 85 of 276

A Helmholtz coil has a 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 the magnetic field at P,P, midway between the centres AA and C,C, is given by [Refer to figure given below]:

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Answer: (D) 8Nμ0I53/2R\dfrac{8N{\mu }_{0}I}{{5}^{3/2}R}

Magnetic field at point P, due to both coils, Bp=2[μ0NIR22(R2+R24)3/2]=μ0NIR253/28R3=8Nμ0I53/2R{B}_{p}=2\left[\dfrac{{\mu }_{0}NI{R}^{2}}{2{\left({R}^{2}+\dfrac{{R}^{2}}{4}\right)}^{3/2}}\right]=\dfrac{{\mu }_{0}NI{R}^{2}}{\dfrac{{5}^{3/2}}{8}{R}^{3}}=\dfrac{8N{\mu }_{0}I}{{5}^{3/2}R}.

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