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{\text{a}} {2} and 2a respectively, from the axis of the wire is:

  • Option 1)

    \frac{\text{1}} {4}

  • Option 2)

    \frac{\text{1}} {2}

  • Option 3)

    1

  • Option 4)

    4

 

Answers (1)

 

For Infinite Length -

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

B=frac{mu_{o}}{4pi}: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)

\frac{\text{1}} {4}

This is incorrect option

Option 2)

\frac{\text{1}} {2}

This is incorrect option

Option 3)

1

This is correct option

Option 4)

4

This is incorrect option

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