The magnetic field induction at a point 4 cm from a long current-carrying wire is 10^-3 T. The magnetic field induction at a distance of 2 cm from the same current-carrying wire will be:

Concept:

Ampere's law : 

It states that the magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.

The magnetic field due to long  straight wire is given by;

\({\rm{B}} = \frac{{{{\rm{\mu }}_0}{\rm{I}}}}{{2{\rm{\pi R}}}}\)

Where B = strength of magnetic field, I = current, R = radius or distance.

Explanation:

Given:

R₁ = 4 cm = 0.04 m, R₂ = 2 cm = 0.02 m, B₁ = 10^-3

So as from the Amperes law

\( \frac{{{B_1}}}{{{B_2}}} = \frac{{{R_2}}}{{{R_1}}}\)

\( {B_2} = {B_1}\frac{{{R_1}}}{{{R_2}}} \)

\( {B_2} = {10^{ - 3}}\times \frac{4}{{2}} = 2\times {10^{ - 3}}\;T \)