Solenoids produce magnetic fields that are relatively intense for the amount of

Question

Solenoids produce magnetic fields that are relatively intense for the amount of current they carry. To make a direct comparison, consider a solenoid with 54 turns per centimeter, a radius of 1.05cm , and a current of 0.610A .

Part A:
Find the magnetic field at the center of the solenoid.
I got

Part B
What current must a long, straight wire carry to have the same magnetic field as that found in part A? Let the distance from the wire be the same as the radius of the solenoid, 1.05cm .

I= ___ A

I need help understanding part b! Thanks in advance!

Explanation / Answer

(a)B = (?0NI) / L
where
?0 = 4? x 10-7
N /L= # turns/length(which is given)=54turns/cm=5400turns/m
B = [(4? x 10-7)(5400 turns/m)(.610A)]
=4.14e-3 T

(b)In case of a wire

where
?0 =4? x 10-7
I=current thru the wire
r=distance of the point (where field is to be calculated)from thewire=1.05cm=0.0105m

4.14e-3=(4? x10-7 x I)/(2 x ? x 0.0105)
I=217.32 A

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