# Easy Ampere's Law Problem

1. Oct 16, 2009

### TwinGemini14

An infinitely long solid conducting wire of radius a = 2 cm centered on the z-axis carries a current I1 = 5 A out of the screen. The current is uniformly distributed over the cross-section of the wire. Co-axial with the wire is an infinitely long thin cylindrical conducting shell of radius of b = 5 cm that carries a current of I2 = 4 A into the screen.

http://i662.photobucket.com/albums/uu347/TwinGemini14/Ampere.gif

1) At x = 1 cm, y = 0 (within the central wire), the magnetic field points

A) in the +x direction.
B) in the +y direction.
C) in the -y direction.

:: This should be B, in the +y direction. Use the right hand rule. Current is going out of the page and curl fingers to show that at (1,0), it should point 'up'.
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2) In the region a < r < b (between the central wire and the thin shell), the magnitude of the magnetic field

A) is constant.
B) is porportional to r.
C) is proportional to 1/r.

:: I'm not sure how to explain it, but my gut feeling is that it is proportional to r. So B.
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3) At x = 6 cm, y = 0 (outside of the shell), the magnetic field points

A) in the -x direction.
B) in the +y direction.
C) in the -y direction.

:: This is very similar to question 1. The answer should be C. Use the right hand rule and notice that at (6,0), the field points 'down'.
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4) What is the magnitude of the magnetic field at x = 1 cm, y = 0 (within the central wire)?

A) 5 µT
B) 10 µT
C) 15 µT
D) 20 µT
E) 25 µT

:: This one I cannot seem to figure out. HELP NEEDED HERE. I've tried finding the current density at a radius of x=1 and using ampere's law, but cannot seem to come to one of the 5 options. Any advice?

B = (4pi*10^-7)(pi*(0.01^2)) / (2pi * 0.01) = 3.14*10^-8 WRONG!!!
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5) What is the magnitude of the magnetic field at x = 6 cm, y = 0 (outside of the shell)?

A) 0.78 µT
B) 3.33 µT
C) 4.51 µT
D) 8.20 µT
E) 12.7 µT

:: B = ((4pi*10^-7)*(Ienclosed))/(2pi*r)
B = (4pi*10^-7)*(5-4) / (2pi * 0.06)
B = 3.33*10^-6