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Two identical circular wires P and Q eac...

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.

Text Solution

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`B=sqrt(B_(1)^(2)+B_(2)^(2)) implies B_(1)=(mu_(0)n_(1)I_(1))/(2a_(1)), B_(2)=(mu_(0)n_(2)I_(2))/(2a_(2))`

If two circular coils of radii `a_(1) " and " a_(2)` having `n_(1) " and " n_(2)` turns carry currents `I_(1) " and " I_(2)` are placed, such that their planes are inclined at an angle `theta` and centres coinciding
`B=sqrt(B_(1)^(2)+B_(2)^(2)+2B_(1)B_(2) cos theta)`
The direction of magnetic field
`B=(mu_(0)n I)/(sqrt(2)a)(1+cos q)`.
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