Question

A straight wire of length 0.53 m carries a conventional current of 0.2 amperes. What is the magnitude of the magnetic field made by the current at a location 2.0 cm from the wire? Use both the exact formula and the approximate formula to calculate the field. (a) result using exact formula

Answer 1

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 :

$B=\dfrac{\mu_oI}{2\pi r}$

$B=\dfrac{4\pi \times 10^{-7}\times 0.2\ A}{2\pi \times 0.02\ m}$

B = 0.000002 T

$B=10^{-5}\ T$

(2) Exact formula:

$B=\dfrac{\mu_oI}{2\pi r}\dfrac{l}{\sqrt{l^2+4r^2} }$

$B=\dfrac{\mu_o\times 0.2\ A}{2\pi \times 0.02\ m}\times \dfrac{0.53\ m}{\sqrt{(0.53\ m)^2+4(0.02\ m)^2} }$

B = 0.00000199 T

or

B = 0.000002 T

Hence, this is the required solution.