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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 16A, coil Y has 25 turns and carries a current of 18 A. The sense of the current in X in antoclockwise, and clockwise in Y, for an observer looking at hte coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre. |
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Answer» Solution :For coil X : `R_1= 16 cm = 0.16 m , N_1 = 20, I_1 = 16A` `:.` Magnetic field at the centre of coil X `B_1 = (mu_0 N_1 I_1)/(2 R_1) = (4 pi xx 10^(-7) xx 20 xx 16)/(2 xx 0.16) = 4pi xx 10^(-4) T` As per right HAND palm rule, `B_1` is DIRECTED horizontally towards the east. For coil `Y: R_2 = 10 cm = 0.10 m , N_2 = 25, l_2 = 18 A` `:. B_2 = (mu_0 N_2 I_2)/(2 R_2) = (4 pi xx 10^(-7) xx 25 xx 18)/(2 xx 0.10) = 9 pi xx 10^(-4) T` As per right hand plam rule, `B_2` is directed horizontally towards WEST. `:.` Net magnetic field B at the centre point in westward direction and is given as : `B = B_2 - B_1 = (9 pi xx 10^(-4) - 4 pi xx 10^(-4)) T = 5 pi xx 10^(-4) T ~= 1.6 xx 10^(-3) T` towards west. 
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