Question

Two identical coils each of radius $R$ and each carrying a current $I$ in the same direction are placed along a common axis and separated by distance $R$. At the midpoint between the two coils the

• A. Magnetic field is zero
• B. Magnetic field is $0.8\sqrt{0.8}{\mu }_{0}I/R$
• C. Second derivative of magnetic field $d^{2}B/d{x}^2=0$
• D. First derivative of magnetic field $dB/dx=0$

Answer 1

Answer: (B)

Magnetic field is $0.8\sqrt{0.8}{\mu }_{0}I/R$

Magnetic field at the mid point between the two coils,
$B=\frac{8{\mu }_{0}NI}{5\sqrt{5}R}$
$B=0.716\frac{{\mu }_{0}NI}{R}$
$B=0.716\frac{{\mu }_{0}I}{R}(\because N=1)$
$B=0.8\sqrt{0.8}\frac{{\mu }_{0}I}{R}$.