# Find magnetic induction

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Two circular coils of wire each having a radius of 4cm and 10 turns have a common axis and are 6cm apart. If a current of 1A passes through each coil in the opposite direction find the magnetic induction:

(i) At the centre of either coil

(ii) At a point on the axis, mid way between them

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(a) The magnetic field due to a current carrying coil at the axis of the coil at a distance x from the centre of coil having N turns is given by

so here I = 1 A, N = 10, r = 4 × 10−2m and x = 6 × 10−2m

And magnetic field due to other coil at the centre is

and since the current in both coil are same but in the opposite direction so magnetic fields at the centre of either coils would be opposite so net magnetic field at the centre of either coil is

(b) The magnetic field at the midway of the two centres would be zero because magnetic field at this point due to both coil is equal but opposite due to opposite current owing in the coils. Thus B=0