A long straight wire of radius a carries a steady current 1. The...

A long straight wire of radius a carries a steady current 1. The current is uniformly distributed across its cross section. The ratio of the magnetic field at

\frac{\mathrm{a}}{2}

and 2a from axis of the wire is:

Options

A $1: 4$
B $4: 1$
C $1: 1$
D $3: 4$

Correct answer

C. $1: 1$

Step-by-step solution

Magnetic field due to straight wire,

B=\frac{\mu_0 I}{2 \pi r}

Magnetic field at

\frac{a}{2}

is,

\mathrm{B}_{\mathrm{a} / 2}=\frac{\mu_0

\mathrm{I}

}{2 \pi(\mathrm{a} / 2)}\therefore \frac{\mathrm{B}_{\mathrm{a} / 2}}{\mathrm{ B}_{2 \mathrm{a}}}=\frac{1}{1}=1: 1

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