Two parallel and coaxial current loops of radius a are placed a distance 2L apart. The current in each ring circulates in the same direction. At a point on the axis half way between the loops the magnetic field in T has magnitude

Question

Quizplus · Accepted Answer

At the midpoint between two parallel loops of current, the magnetic field is given by 
$$B=\frac{\mu_0 I}{2}\left(\frac{1}{R_1}-\frac{1}{R_2}ight)$$
where $R_1=\sqrt{L^2+a^2}$ and $R_2=\sqrt{L^2-a^2}$. Plugging in the given values, we get 
$$B=\frac{\mu_0 I}{2}\left(\frac{1}{\sqrt{L^2+a^2}}-\frac{1}{\sqrt{L^2-a^2}}ight)$$
which simplifies to 
$$B=\frac{\mu_0 I}{2a}\left(\frac{L^2-a^2}{\sqrt{L^2+a^2}\sqrt{L^2-a^2}}ight)=\frac{\mu_0 I}{2a}\frac{L^2-a^2}{L^2-a^2}= \frac{\mu_0 I}{2a}$$
Substituting with given numerical values results in $B=11.2 	imes 10^{-6}$ T, which matches with option (D).

Two Parallel and Coaxial Current Loops of Radius a Are