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  • Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The

4.14) Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

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Using the right-hand thumb rule we can see that the direction of the magnetic field due to coil X will be towards the east direction and that due to coil Y will be in the West direction.

We know the magnetic field at the centre of a circular loop of radius r carrying current I is given by

B=\frac{\mu _{o}I}{2r}

\\B_{x}=\frac{n_{x}\mu _{o}I_{x}}{2r_{x}}\\ \\B_{x}=\frac{20\times 4\pi \times 10^{-7}\times 16}{2\times 0.16}

\\B_x=4\pi\times 10^{-4}T(towards East)

\\B_{y}=\frac{n_{y}\mu _{o}I_{y}}{2r_{y}}\\ \\B_{y}=\frac{25\times 4\pi \times 10^{-7}\times 18}{2\times 0.1}

\\B_y=9\pi \times10^{-4}T(towards west)

The net magnetic field at the centre of the coils,

Bnet=By - Bx

=1.57\times10-3 T 

The direction of the magnetic field at the centre of the coils is towards the west direction.

 

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Sayak

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