Discussion Forum

1)

A circular wire loop of radius R is placed in the x-y plane centred at the origin O. A square loop of side a(a<< R) having two turns is placed with its centre at, $z=\sqrt{3} R$ along the axis of the circular wire loop, as shown in figure. The plane of the

 

 

the square loop makes an angle of $45^{0}$with respect to the z-axis. If the mutual inductance between the loops is given by 

 $\frac{\mu_{0}a^{2}}{2^{p/2}R}$, then the value of p is 

Answer:

Option B

Explanation:

If l current flows through the circular loop, then magnetic flux at the location of square loop is

$B=\frac{\mu_{0}IR^{2}}{2(R^{2}+Z^{2})^{3/2}}$

 Substituting the value of Z=$(\sqrt{3}R)$, we have

  $B= \frac{\mu_{0}I}{16 R}$

Now, total flux through the square loop is

$\phi_{T}=NBS \cos \theta$

=$=(2)\left(\frac{\mu_{0}T}{16R}\right)a^{2} \cos 45^{0}$

Mutual inductance

     $M=\frac{\phi_{T}}{l}=\frac{\mu_{0}a^{2}}{2^{7/2}R}$

 $\therefore$   p=7