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 :
![B=\dfrac{\mu_oI}{2\pi r}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Cmu_oI%7D%7B2%5Cpi%20r%7D)
![B=\dfrac{4\pi \times 10^{-7}\times 0.2\ A}{2\pi \times 0.02\ m}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%200.2%5C%20A%7D%7B2%5Cpi%20%5Ctimes%200.02%5C%20m%7D)
B = 0.000002 T
![B=10^{-5}\ T](https://tex.z-dn.net/?f=B%3D10%5E%7B-5%7D%5C%20T)
(2) Exact formula:
![B=\dfrac{\mu_oI}{2\pi r}\dfrac{l}{\sqrt{l^2+4r^2} }](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Cmu_oI%7D%7B2%5Cpi%20r%7D%5Cdfrac%7Bl%7D%7B%5Csqrt%7Bl%5E2%2B4r%5E2%7D%20%7D)
![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} }](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Cmu_o%5Ctimes%200.2%5C%20A%7D%7B2%5Cpi%20%5Ctimes%200.02%5C%20m%7D%5Ctimes%20%5Cdfrac%7B0.53%5C%20m%7D%7B%5Csqrt%7B%280.53%5C%20m%29%5E2%2B4%280.02%5C%20m%29%5E2%7D%20%7D)
B = 0.00000199 T
or
B = 0.000002 T
Hence, this is the required solution.
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