Question

Two concentric coils X and Y of radii 16 cm and 10 cm lie in the same vertical plane containing N-S direction. X has 20 turns and carries 16 A. Y has 25 tums & carries 18 A. X has current in anticlockwise direction and Y has current in clockwise direction for an observer, looking at the coils facing the west.

• A. $5\pi \times {10}^{-4}T$ towards west
• B. $13\pi \times {10}^{-4}T$ towards east
• C. $13\pi \times {10}^{-4}T$ towards west
• D. $5\pi \times {10}^{-4}T$ towards east

Answer 1

The correct option is A $5\pi \times {10}^{-4}T$ towards west

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$\begin{array}{c}Accordingtoquestion...............\\ \underset{–}{forcoilX,}\\ Radiusofcoil,r_X=16cm=0.16m\\ Numberofturns,N_X=20\\ currentpas\sin gthroughcoil,L_X=16A\\ MagneticfieldatthecentreofcoilXis:\\ B_X=\frac{{\mu }_0{L}_X{N}_X}{2r_X}\\ =\frac{4\pi \times {10}^{-7}\times 16\times 20}{2\times 0.16}\\ =4\pi \times {10}^{-4}T\\ and,\\ \underset{–}{forcoilY},\\ Radiusofcoil,r_Y=10cm=0.10m\\ Numberofturns,N_Y=25\\ currentpas\sin gthroughcoil,L_Y=18A\\ MagneticfieldatthecentreofcoilYis:\\ B_Y=\frac{{\mu }_0{L}_Y{N}_Y}{2r_Y}\\ =\frac{4\pi \times {10}^{-7}\times 18\times 25}{2\times 0.10}\\ =9\pi \times {10}^{-4}T\\ hence,\\ Netmagneticfield=B_Y-B_X\\ =9\pi \times {10}^{-4}-4\pi \times {10}^{-4}\\ \therefore 5\pi \times {10}^{-4}T\\ sothecorrectoptionisA.\end{array}$