A long straight wire of radius a carries a steady current I The current is uniformly distributed over its $$cross-section$$. The ratio of the magnetic fields B and B', at radial distances $$a2$$ and $$2a$$ respectively, from the axis of the wire is

Question

A long straight wire of radius a  carries a steady current I  The current is uniformly distributed over its $$cross-section$$. The ratio of the magnetic fields B  and B', at radial distances $$a2$$ and $$2a$$ respectively, from the axis of the wire is

Infinity Learn · Accepted Answer

Magnetic field at a point inside the wire at distance $$r=a2$$ from the axis of wire is $$B=$$μ$$0I2$$$$π$$$$a2r=$$μ$$0I2$$$$π$$$$a2$$×$$a2=$$μ$$0I4$$$$π$$aMagnetic field at a point outside the wire at distance $$r(=2$$ $$a)$$ from the axis of wire isB'$$=$$μ$$0I2$$$$π$$$$r=$$μ$$0I2$$π×$$12a=$$μ$$0I4$$$$π$$a  ∴ BB'$$=1$$

A long straight wire of radius $a$ carries a steady current $I$ The current is uniformly distributed over its cross-section. The ratio of the magnetic fields $B$ and $B^{'}$ , at radial distances $\frac{a}{2}$ and $2 a$ respectively, from the axis of the wire is

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A long straight wire of radius a carries a steady current I The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances a2 and 2a respectively, from the axis of the wire is

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Ready to Test Your Skills?

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A long straight wire of radius $a$ carries a steady current $I$ The current is uniformly distributed over its cross-section. The ratio of the magnetic fields $B$ and $B^{'}$ , at radial distances $\frac{a}{2}$ and $2 a$ respectively, from the axis of the wire is