Question

A current loop consists of two identical semicircular parts each of radius r, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i. The resultant magnetic field due to the two semicircular parts at their common centre i

Answer 1

Magnetic field due to cCrcular Current Carrying arc -

B=frac{mu_{o}}{4pi}:frac{2pi i}{r}=frac{mu_{o}i}{2r}

- wherein

\vec{B_{1}} due to loop in XY plane is in Z direction

\vec{B_{2}} due to loop in XZ plane is along Y direction

\vec{B}=B_{1}\hat{k}+B_{2}\hat{j}

\Rightarrow \left | \vec{B} \right |=\sqrt{B_{1}^{2}}+{B_{2}^{2}}= \sqrt{2}B

\left | \vec{B} \right |=\sqrt{2}.\left ( \frac{\mu _{0}I}{4R} \right )

=\frac{\mu _{o}I}{2\sqrt{2}R}

Option 1)

\frac{\mu_{o}i}{\sqrt{2}R}

Incorrect Option

Option 2)

Correct Option

Option 3)

\frac{\mu_{o}i}{2R}

Incorrect Option

Option 4)

\frac{\mu_{o}i}{{4}R}

Incorrect Option