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Question
Two identical circular wires P and Q each of radius R and carrying current ‘I’ are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.
Solution
Magnetic field at centre of circular loop carrying current I given
`B =(mu_0 I)/(2a)`
Here, a = R
Now, magnetic field due to loop Q
`B_Q = B_x = (mu_0I)/(2R)`
Magnetic field due to loop P.
`B_p = B_y = (mu_0I)/(2R)`
Net field at centre.
`B_N = sqrt(B_p^2 + B_Q^2)`
`= sqrt(((mu_0I)/(2R))^2 +sqrt(((mu_0I)/(2R))^2`
`(mu_0I)/(2R)sqrt2`
`B_N (mu_0I)/(sqrt2R)`
Direction of net magnetic field
tan`theta = B_p/B_Q =1`
`theta =pi/4`
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