Answer:
The magnetic field at 0.01m from the wire is 0.2T.
Explanation:
The magnetic field [tex]B[/tex] at a distance [tex]R[/tex] due to a straight wire carrying a current [tex]I[/tex] is
[tex]B = \dfrac{\mu_oI }{2\pi R},[/tex]
where [tex]\mu_o = 4\pi*10^{-7} m\cdot kg\cdot s^{-2} A^{-2}[/tex] is the magnetic constant.
Now, we are told that the magnetic field from a wire at [tex]R = 0.02m[/tex] is [tex]B = 0.01[/tex]; therefore,
[tex]0.1T = \dfrac{(4\pi*10^{-7})I }{2\pi (0.02m)},[/tex]
solving for [tex]I[/tex] we get:
[tex]I = 10,000A[/tex]
which is the current through the wire.
Now, the magnetic field [tex]B[/tex] of the wire due to this current at the distance of [tex]R = 0.01m[/tex] is
[tex]B =\dfrac{(4\pi*10^{-7})(10,000)}{2\pi (0.01)}[/tex]
[tex]\boxed{B = 0.2 T}[/tex]
Thus, the magnetic field at 0.01m from the wire is 0.2T.
