Question

The current in a solenoid with 23 turns per centimeter is 0.45A . The solenoid has a radius of 1.6cm . A long, straight wire runs along the axis of the solenoid, carrying a current of 15A .
Part A
Find the magnitude of the net magnetic field a radial distance of 0.80cm from the straight wire.

Answer 1

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Answer 2

given, n (no. of turns per meter ) = 23 * 1000 = 23000
I' (current through the solenoid) = 0.45A
R (radius of the solenoid) = 1.6 cm= 1.6/100 m
I''(current through the straight wire) = 15A
r (distance of the point from the wire) = 0.8 cm = 0.8/100 m


Let B' be the magnetic field of the solenoid.
\[B' = \mu nI' = 4 \pi * 10^{-7} * 23 * 10^{2} * 0.45\]
B' = 1.29 * 10^-6 T

Let B'' be the magnetic field of the long wire
\[B'' = \frac{ \mu I'' }{ 2\pi r} = \frac{ 4\pi * 10^{-7} * 15 }{ 2\pi * 0.8 * 10 ^{-2} }\]
B'' = 3.75 * 10^-4 T
The total magnetic field is

B = B' + B'' =1.29 * 10^-6 + 3.75 * 10^-4 = 3.7629 * 10^-4 T