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Question
Two identical circular loops, P and Q, each of radius r and carrying equal currents are
kept in the parallel planes having a common axis passing through O. The direction of current in P is clockwise and in Q is anti-clockwise as seen from O which is equidistant from the loops P and Q. Find the magnitude of the net magnetic field at O.
Solution
The standard formula for field at an axial point is given as
`B=(mu_0ia^2)/(2(a^2 +d^2)^(2/3))`
So, in this case
`B = (mu_0Ir^2)/(2(r^2 +((2r)/2)^2)^(3/2)) = (mu_0I)/((2)^(5/2)r)`
Now, as the current flowing in loop P is clockwise by using right hand thumb’s rule the direction of the magnetic field will be towards left and as the current in loop Q is clockwise then the direction of magnetic field is towards left. So the net magnetic field at point O will be the sum of the magnetic fields due to loops P and Q.
Also, as the fields produced are at an equal distance to O, BP = BQ,
So, net field
`B=B_P+B_Q= 2(mu_0I)/((2)^(5/3)r) = (mu_0I)/((2)^(3/2)r)`
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