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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.
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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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