An infinitely long current carrying wire is placed along $$X-axis$$ and magnetic induction produced by this wire at point p, which lies in XY plane is $$1$$ T. When the same wire is placed along $$Y-axis$$, magnetic induction at the same point is found to be $$3T$$ . What will be the magnetic induction at the same point p when the same current carrying wire is placed along $$Z-axis$$?

Question

An infinitely long current carrying wire is placed along $$X-axis$$ and magnetic induction produced by this wire at point p, which lies in XY plane is $$1$$ T. When the same wire is placed along $$Y-axis$$, magnetic induction at the same point is found to be $$3T$$ . What will be the magnetic induction at the same point p when the same current carrying  wire is placed along $$Z-axis$$?

Infinity Learn · Accepted Answer

$$r=x2+y2B1=$$μ$$0i2$$$$π$$$$y=ky$$⇒$$y=kB1B2=$$μ$$0i2$$$$π$$$$x=$$$$kx$$⇒$$x=kB2$$∴$$B3=$$μ$$0i2$$$$π$$$$r=kkB22+kB12=B1B2B12+B22=1$$×$$31+3T$$∴$$B3=32T$$

Magnetic field due to a straight current carrying wire

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Magnetic field due to a straight current carrying wire

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r=x2+y2B1=μ0i2πy=ky⇒y=kB1B2=μ0i2πx=kx⇒x=kB2∴B3=μ0i2πr=kkB22+kB12=B1B2B12+B22=1×31+3T∴B3=32T

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