A very long coaxial cable consists of a solid cylindrical innerconductor of radius 3.8mm , surrounded by an outer cylindricalconductor with inner radius 7mm , and outer radius 9.3mm . Theregion between the two conductors is filled with a waxlikeinsulating material to keep the conductors from touching eachother. The inner conductor carries a current 4.65A , into the page,while the outer conductor carries a current 4.6A , out of thepage.
Part A
Use Amp�re's law to derive an expression for the magnetic fieldas a function of r(the distance from the central axis) atpoints between the two conductors(R1<r<R2i). Use thisexpression to find the magnetic field at 4.8mm .
| B = | 1.94�10^(-4) | T [I GOT THIS PARTCORRECT] |
Use Amp�re's law to derive an expression for the magnetic fieldas a function of r(the distance from the central axis) atpoints inside the outer conductor(R2i<r<R2o). Usethis expression to find the magnetic field at 7.1mm .
Use into page as negative and out of page as positivecurrent.
Comment
Hint 1. Ampere's Law
Ampere's Lawstates:Â Â ?B??s=?0?IenclosedTherefore you need to figure out what the enclosed current is forthis case.
Hint 2. Enclosed current
The enclosed current is the current in the inner conductor +that portion of the current enclosed in the outer conductor. UseItotal/Atotal=Ienclosed/AenclosedDon't forgetAtotal=pi?(R22o?R22i)and there is a corresponding expression forAenclosed.
