Find the magnetic induction at origin in the figure shown

1.	Find the magnetic induction at origin in the figure shown
Answer» In this figure the magnetic field due to all wires passing through origin and directed towards origin is zero. And due to the circular path in first quadrant is that we integrate Biot savart law from o to πr/2 we get µ.I/8r And due to the circular path in 2nd quadrant is same but the r is double. µ.I/16r And due to wire in the 3rd quadrant is we can't say as the angle is unknown. apply the formula of straight wire and calculate that. Total magnetic induction is the sum of the 3 equations obtained.

Answer»

In this figure the magnetic field due to all wires passing through origin and directed towards origin is zero.

And due to the circular path in first quadrant is that we integrate Biot savart law from o to πr/2

we get µ.I/8r
And due to the circular path in 2nd quadrant is same but the r is double.
µ.I/16r
And due to wire in the 3rd quadrant is we can't say as the angle is unknown.
apply the formula of straight wire and calculate that.

Total magnetic induction is the sum of the 3 equations obtained.

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