Explanation:
It is given that,
Length of wire, l = 0.53 m
Current, I = 0.2 A
(1.) Approximate formula:
We need to find the magnitude of the magnetic field made by the current at a location 2.0 cm from the wire, r = 2 cm = 0.02 m
The formula for magnetic field at some distance from the wire is given by :
[tex]B=\dfrac{\mu_oI}{2\pi r}[/tex]
[tex]B=\dfrac{4\pi \times 10^{-7}\times 0.2\ A}{2\pi \times 0.02\ m}[/tex]
B = 0.000002 T
[tex]B=10^{-5}\ T[/tex]
(2) Exact formula:
[tex]B=\dfrac{\mu_oI}{2\pi r}\dfrac{l}{\sqrt{l^2+4r^2} }[/tex]
[tex]B=\dfrac{\mu_o\times 0.2\ A}{2\pi \times 0.02\ m}\times \dfrac{0.53\ m}{\sqrt{(0.53\ m)^2+4(0.02\ m)^2} }[/tex]
B = 0.00000199 T
or
B = 0.000002 T
Hence, this is the required solution.
