Two wires CO and OA carry equal currents...

Two wires CO and OA carry equal currents I as shown in figure. One end of both the wires extends to infinity. Given `/_AOC=theta`. What is the magnitude of magnetic field induction at a point P at a distance r from O lying on the bisector of angle `theta`.

Text Solution

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`a=r sin (theta//2)`
Magnetic field induction at P due to current through CO and OA is
`B=2[(mu_0)/(4pi)I/a[sin(90-theta//2)+sin 90^@]]=(mu_0)/(2pi)(I(1+cos theta//2))/(r sin theta//2)`

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`(mu_0)/(2pi) i/r (1+cos(alpha)/2)/(sin(alpha/2))`

`(mu_0)/(4pi) i/r ((alpha)/2)`

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zero

`mu_(0)I//2pir`

`(mu_(0)I)/(2pir)(1+1/(sqrt(2)))`

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An infinitely long wire carrying current I is along Y-axis such taht its one end is at point A(0,b) while the wire extends upto +oo . The magnitude of magnetic field strength at point (a,0) is

`(mu_0I)/(4pia)(1+b/(sqrt(a^2+b^2)))`

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none of these