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Question
Two identical circular loops P and Q, each of radius R carrying current I are kept in perpendicular planes such that they have a common centre O as shown in the figure.
Find the magnitude and direction of the net magnetic field at point O.
Solution
In the P coil, the current is in an anticlockwise direction. So the magnetic field (BP) will be in the direction shown.
Similarly, in Q the direction of magnetic field BQ will be shown (from Flemings left-hand rule) the resultant of BP and BQ will be B.
So `B = sqrt(B_P^2 + B_Q^2)`
BP = BQ
because both the coil has the same current and the same radius.
`B = sqrt(B_P^2 + B_P^2) = sqrt2B_P`
∵ `B_P = (mu_0I)/(2R)`
`B = sqrt2((mu_0I)/(2R))`
⇒ B = `(mu_0I)/(sqrt2R)`
The net magnetic field is oriented to both fields at 45°.
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