Question

2 identical circular loop P and Q carrying equal amount of current are placed such that their geometrical axis are perpendicular to each other. the direction of current appear anticlockwise when seen from O which is equidistant from loop P and Q. find the magnitude and direction. of the net magnetic field. ?

Answer 1

$$\begin{gathered} Magneticfieldatthepointontheaxisofthecircularloop, \\ B=\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{{\left(Z^2+R^2\right)}^{3/2}} \\ Zisthedis\tan ceofthepointfromthecentreofloop \\ Ristheradiusoftheloop. \\ SInceboththeloopareperpendicualrhencemagneticfieldatpointOduetoboththeloopwillbeperpendicular. \\ {B}_1=\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{{\left(Z^2+R^2\right)}^{3/2}} \\ {B}_2=\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{{\left(Z^2+R^2\right)}^{3/2}} \\ B=\sqrt{{B_1}^2+{B_2}^2}=\sqrt{2}\left(\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{{\left(Z^2+R^2\right)}^{3/2}}\right) \\ Directionofnetmagneticfield. \\ \tan \theta =\frac{B_2}{B_1}=\frac{\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{{\left(Z^2+R^2\right)}^{3/2}}}{\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{{\left(Z^2+R^2\right)}^{3/2}}}=1 \\ \theta =45degree,whichistheanglebetweenresulatntmagneticfieldandaxisoftheeitherlop. \end{gathered}$$