https://chip.physics.purdue.edu/protected/Halliday6EMimg/h32s42.jpg Two wires, p
ID: 1283852 • Letter: H
Question
https://chip.physics.purdue.edu/protected/Halliday6EMimg/h32s42.jpg
Two wires, parallel to the z axis and distance 4r apart, carry equal currents I =0.63 A in opposite directions, as shown in Fig. 32-40. A circular cylinder of radius r and length L=8 cm has its axis on the z axis, midway between the wires. Use Gauss' law for electromagnetism to calculate the net outward magnetic flux through the half of the cylindrical surface above the x axis. (Hint: Find the flux through that portion of the xz plane that is within the cylinder. )
Explanation / Answer
The answer starts at "Take the integral of the above from 1r to 3r" , the setting up starts next line.
? = (A)*(B)*(n)*cos(?) where
A is the area of the half circle
B is the magnetic field
n is the number of wires
Derive the formula to get
d? = [2*?*I*L*dx*cos(?)] / [2*?*x] where
cos(?) is 1
Take the integral of the above from 1r to 3r
[ (2*?*I*L) / (2*?) ] * ln(3)
remember ? is 4? X 10^-7
And that's your answer.
There shouldn't be a need to convert the units with the way I did it.
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