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What is the magnitude of magnetic field ...

What is the magnitude of magnetic field at the centre O of loop of radius `sqrt2 m` made of uniform wire when a current of 1amp entres in the loop and taken out of it by two long wires as shown in the Fig.

Text Solution

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`vecB_1`=Magnetic field due to left wire
`B_1=(mu_0I)/(4pid)(sin pi/2-sin pi/4) hatk`
`vecB_2`=Megnetic field due to right
wire
`=(mu_0I)/(4pid)(sin pi/2-sin pi/4)(-hatk)`

In circular wire, `I prop1/R implies(I_1)/(I_2)=theta/(2pi-theta)`
`:. I_1=(theta/(2pi-theta))I_2`
`:. vecB_3`=Magnetic field due to circular
wire
`=(mu_0I_1 theta)/(4pir)-(mu_0I_2(2pi-theta))/(4pir)`
`=(mu_0I_2 theta)/(4pir)-(mu_0 theta(2pi-theta))/(4pir(2pi-theta))I_2=0`
`:. vecB=vecB_1+vecB_2+vecB_3=0`
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