Question

Two identical circular coils each of radius \(R\) and number of turns \(N\) are arranged coaxially with a separation of \(R\) between their centers. If the current through each coil is \(I\), then the maximum resultant magnetic field induced at the midpoint of the line joining the centers of the two coils is

• A. \(\dfrac{2\mu_0NI}{R}\)
• B. \(\dfrac{4\mu_0NI}{5R}\)
• C. \(\dfrac{8\mu_0NI}{5\sqrt5\,R}\)
• D. \(\dfrac{\mu_0NI}{\pi R}\)

Hint:

The magnetic field on the axis of a circular coil is \[ \boxed{ B = \frac{\mu_0NI R^2} {2(R^2+x^2)^{3/2}}. } \] At the midpoint between two identical coaxial coils (Helmholtz arrangement), the magnetic fields add in the same direction.

Answer 1

The Correct Option is C