Question

Q 47. Find out the ratio of the currents through two circular coils of radil 4cm and 16cm both of which are equivalent to magnetic dipole having
equal magnetic moments.​

Answer 1

Answer:

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Explanation:

We know Magnetic field at centre of a coil having  Current I, radius r and number of turns N is given as  B=2rμ0NI 

and at a distance x from the centre and on the axis is B=2(x2+r2)μ0NIx and its direction is given by right-hand screw rule i.e.

 if the observer sees that the current is anticlockwise then the field will be towards the observer and vice-versa, as shown in the figure−1 

Part a 

Field at center O1  will be difference of field due to loop-1 and loop-2 

AtO1  Bnet = 2rμ0NI  - 2(x2+r2)μ0NIx towards observer 

putting μ0=4π×10−7 ,N=6, r=.04 meter ,x= .06 meter and I = 1 all units in S.I. system

we get Bnet=5.07×10−5 Tesla towards the observer

Similarly, AtO1 the filed due to circle 2 will dominate so net filed will be 

Bnet=5.07×10−5 Tesla in a direction away  from the observer.

Part b 

According to the above theory the field at the midpoint on the axis of joining the centres will be equal and opposite as current in loops is opposite so net field is zero there at O 

Answer 2

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