A long straight wire of radius a carriesa stead current i . The current is uniformly distributed across its cross section. The ratio of the magnetic field at  a/2 \; and \; 2a\; is

  • Option 1)

    1/2

  • Option 2)

    1/4

  • Option 3)

    4

  • Option 4)

    1

 

Answers (1)

As we learnt in

Magnetic field Inside the solid cylinder -

B= \frac{\mu _{o}}{2\pi } \frac{ir}{R^{2}}

- wherein

 

 

Uniform current is flowing. Current enclosed in the 1st ampèrean path is  \frac{I.\pi r_{1}\, ^{2}}{\pi R^{2}}=\frac{Ir_{1}\, ^{2}}{R^{2}}

\therefore \; \; \; B=\frac{\mu _{0}\times current}{path}=\frac{\mu _{0}.Ir_{1}\, ^{2}}{2\pi r_{1}R^{2}}=\frac{\mu _{0}.Ir_{1}}{2\pi R^{2}}

Magnetic induction at a distance r_{2}=\frac{\mu _{0}.I}{2\pi r_{2}}

\therefore \; \; \; \frac{B_{1}}{B_{2}}=\frac{r_{1}r_{2}}{R^{2}}=\frac{\frac{a}{2}.2a}{a^{2}}=1    


Option 1)

1/2

Incorrect option

Option 2)

1/4

Incorrect option

Option 3)

4

Incorrect option

Option 4)

1

Correct option

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