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

Step-by-step 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=(\mu_oI)/(2\pi r)`

`B=(4\pi * 10^(-7)* 0.2\ A)/(2\pi * 0.02\ m)`

B = 0.000002 T

`B=10^(-5)\ T`

(2) Exact formula:

`B=(\mu_oI)/(2\pi r)(l)/(√(l^2+4r^2) )`

`B=(\mu_o* 0.2\ A)/(2\pi * 0.02\ m)* (0.53\ m)/(√((0.53\ m)^2+4(0.02\ m)^2) )`

B = 0.00000199 T

or

B = 0.000002 T

Hence, this is the required solution.