2) The figure shows a cross section of coaxial cable that is infinitely long. A

Question

2) The figure shows a cross section of coaxial cable that is infinitely long. A current I travels along the wall of the smaller cylinder (radius a) into the page. The same amount of current I travels along the wall of the bigger cylinder (radius b), but coming out of the page. The blue regions are insulators and the black circles are crosssections of the conducting coaxial cylinders. The current is uniformly distributed over the conducting cylinders. Since there is current, there will be a magnetic field. The goal of this problem is to calculate the amount of energy stored in the magnetic field. a) Use Ampere

Explanation / Answer

The discussion which accompanies the question tells you what answer (1) is, but the technique being used there is unnecessarily complex. I would answer the question this way - Firstly, I would assume that the questions are asking for the charge density on the inner and outer surfaces of the outer cylinder. For every positive charge on the inner conductor there will be an induced negative charge on the inner surface of the outer cylinder, and for each of these there will be another positive charge on the outer surface of the outer cylinder. In other words, all 3 surfaces will bear a charge of 6nC/m. Take 1m length of the cable. 1) the area of the inner surface will be pi*0.095m^2 and the charge density will be -6/(pi*0.095) = -20.1nC/m^2 2) the area of the outer surface will be pi*0.134m^2 and the charge density will be 6/(pi*0.134) = 14.25nC/m^2 Note that the correct term for this kind of cable is 'coaxial'. It consists of cylinders which have the same axis.

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