Answer to Question #244032 in Atomic and Nuclear Physics for Michael

Question

A coil of wire 7 m long and with 220 turns carries a current of 1.6 A.            

1. What is the magnitude of the magnetic field strength?                   

1. Calculate the flux density if the coil is in a vacuum. 
2. (Permeability of a vacuum is 1.257 × 10^–6H/m.)                       

1. Calculate the flux density inside a bar of carbon steel that is positioned within the coil. 

                                                     

Answer 1

$Part(1)\\B=\frac{\mu_0 NI}{2\pi r}$

$B=\frac{4\pi \times220\times1.6}{2\pi \times7}$

$B=1.0057\times10^{-5}T$

Part(2)

$B=\mu_0H(1+\chi)$

$H=\frac{Ni}{l}$

$H=\frac{220\times1.6}{7}=50.28A/m$

$\chi=\frac{\mu}{\mu_0}-1$

Put value

$$\chi=\frac{1.257\times10^{-6}}{4\pi\times10^{-7}}-1=7.96\times10^{-4}$$

$$B=4\pi\times10^{-7}\times50.28(1+7.96\times10^{-4})$$

$B=6.320\times10^{-6}T$