# 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 and 2a respectively, from the axis of the wire is: Option 1) Option 2) Option 3) 1 Option 4) 4

P Prateek Shrivastava

For Infinite Length -

$\phi_{1}=\phi_{2}=90^{\circ}$

$B=\frac{\mu_{o}}{4\pi}\:\frac{2i}{r}\:$

- wherein

Magnetic field at a point inside the wire at a distance $r=\frac{a}{2}$  from the axis of wire is

$B=\frac{\mu_{o} I}{2\pi a^{2}}r = \frac{\mu_{o} I}{2\pi a^{2}}\frac{a}{2}=\frac{\mu_{o} I}{4\pi a}$

Magnetic field at a point out side the wire at distance r=2a from the axis of wive is

$B^{1}=\frac{\mu_{o} I}{2\pi r} = \frac{\mu_{o} I}{2\pi }\frac{a}{2a}=\frac{\mu_{o} I}{4\pi a}$

$\therefore \frac{B}{B^{1}}=1$

Option 1)

This is incorrect option

Option 2)

This is incorrect option

Option 3)

1

This is correct option

Option 4)

4

This is incorrect option

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