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 is

• A. $\frac{{\mu }_{0}i}{\sqrt{2}R}$
• B. $\frac{{\mu }_{0}i}{2\sqrt{2}R}$
• C. $\frac{{\mu }_{0}i}{2R}$
• D. $\frac{{\mu }_{0}i}{4R}$

Answer 1

The correct option is B $\frac{{\mu }_{0}i}{2\sqrt{2}R}$

Magnetic field due to the two parts at their common centre are respectively,

$B_y=\frac{{\mu }_{0}i}{4R}$ and $B_z=\frac{{\mu }_{0}i}{4R}$

Resultant field $=\sqrt{B_y^2+B_z^2}$

$=\sqrt{{\left(\frac{{\mu }_{0}i}{4R}\right)}^2+{\left(\frac{{\mu }_{0}i}{4R}\right)}^2}$

$=\sqrt{2}.\frac{{\mu }_{0}i}{4R}=\frac{{\mu }_{0}i}{2\sqrt{2}R}$