Question

PLZ HELP
A coaxial cable consists of an inner cylindrical conductor of radius R 1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R 2 = 0.080 m and outer radius R 3 = 0.090 m. The inner conductor carries current I 1 = 1.8 A in one direction, and the outer conductor carries current I 2 = 7.5 A in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ 0 = 4π × 10-7 T · m/A)
At r = 0.060 m (in the gap midway between the two conductors)
and at
r=.150 m (outside the cable)

Answer 1

any ideas

Answer 2

are you looking for a formula to plug some numbers into or are you expected to address Amperes Law and line integrals etc?

Answer 3

either way is fine ... but the answers will obviously be different.

Answer 4

i can use a formula. either way is fine

Answer 5

i think its amperes law

Answer 6

can i see both

Answer 7

i think amperes law

Answer 8

i don't have a formula to hand (Hyperphysics normally does, but it seems to be inaccessible these days) so we should create a formula by looking at some Amperian loops.

will be back in about an hour to post some stuff.

Answer 9

k thanks i think its the whole b=μo i / (2 π r) but im not sure

Answer 10

yes, certainly, outside both wires you should have superposiition.

and if you do that, bearing in mind that the fields cancel out as the currents are travelling in different directions, then you are sorted.

inside the Amperian loops, i am more hesitant as there are more than one. this is really Green's Theorem and I'd need to have a quick go with pen and paper to work it out.

this is where the answer lies:
http://mathinsight.org/greens_theorem_multiple_boundary_components

have to go again. will be back in a while.

Answer 11

thanks we just used the formula in class. no greens thereom

Answer 12

Still need help

Answer 13

sure.

imagining there is no inner conductor, and looking solely at the magnetic field of the hollow outer cylinder, the magnetic field circulating around that hollow outer cylinder should be zero.

this is because there is no current flowing along the inside of the hollow cylinder, so the magnetic field around its internal circumference will be also zero -by Amperes Law. [ ∫B dl = mu ∫∫ J dA = ∑I = 0.]

therefore, "At r = 0.060 m (in the gap midway between the two conductors)", you can ignore the outer conductor and just use the equation for the inner conductor. you quoted that above, i think. you are super imposing fields, but the field from the hollow conductor is zero.

i will add some equations tomorrow. i hope you agree with this conclusion. if not, please correct me.

Ampere Law and Green's theorem are identical for these purposes: http://mathinsight.org/greens_theorem_idea

....will become clear if you look at Maxwell's (Heaviside's) equations for long enough that it is almost all based on Green and divergence theorem.

Answer 14

"imagining there is no inner conductor, and looking solely at the magnetic field of the hollow outer cylinder, the magnetic field circulating around that hollow outer cylinder should be zero. "

clarifying this:

"imagining there is no inner conductor, and looking solely at the magnetic field of the hollow outer cylinder, the magnetic field **within** that hollow outer cylinder should be zero. "

Answer 15

i agree but when i solve i get 1.1*10^-6 from the equation which is incorrect

Answer 16

R u sayin its 0 for the first distance?

Answer 17

hi, i will have a crack at actually doing this now. please give me a while.

Answer 18

6 micro T and 7.6 micro T ??

Answer 19

@akohl