Answer to Question #175128 in Electricity and Magnetism for Joshua Musyoki

Question #175128

A long solenoid of cross-sectional area 28๐‘๐‘š2

A coil ๐ถ of 160 turns of insulated wire is wound tightly around the centre of the solenoid. If ๐‘› is aย 

constant equal to 1.5 ร— 10

3๐‘šโˆ’1

and ๐œ‡๐‘œ is the permeability of free space, calculate for a current ofย 

3.5๐ด in the solenoid; (i) the magnetic flux at the centre of the solenoid. (ii) the flux linkage in theย 

coil ๐ถ. (iii) If the current in the coil ๐ถ is reversed in 0.80๐‘ , calculate the average e.m.f. induced inย 

the coil ๐ถ.


1
Expert's answer
2021-03-29T09:03:51-0400

(i) The magnetic flux at the centre of the solenoid:


"B=\\mu_0nI=4\\pi\u00b710^{-7}\u00b71.5\u00b710^3\u00b73.5=6.6\u00b710^{-3}\\text{ T}."

(ii) The flux linkage in theย coil ๐ถ:


"\\Phi=BAN=6.6\u00b710^{-3}\u00b725\u00b710^{-4}\u00b7160=\\\\=3\u00b710^{-3}\\text{ Wb}."


(iii) If the current in the coil ๐ถ is reversed in 0.80๐‘ , calculate the average e.m.f. induced inย the coil ๐ถ:


"\\text{e.m.f.}=\\frac{\\Delta \\Phi}{\\Delta t}=\\frac{2\\Phi}{\\Delta t}=7.5\u00b710^{-3}\\text{ V}."



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