Two thin conducting concentric cylinders have infinite length. The inner cylinde
ID: 2236107 • Letter: T
Question
Two thin conducting concentric cylinders have infinite length. The inner cylinder has a radius a and a line charge density lambda. The outer cylinder is uncharged and has a radius of b. (a) Find the electric field a distance r from the axis, in the region where r>b. (b) By direct integration, find the work required to move a small charge q from the radius, r in part a and the inner cylinder. (c) Using the results of part b, find the potential difference between the two cylinders.Explanation / Answer
This is a very lengthy problem so I'll only outline the procedure. 1) Use gauss's law to find the E-field between the cylinders ;b > r >a, Use Gauss's law to find the E-field outside the cylinders; r > c The field in the conductors is zero. 2) Now integrate Edr from the origin out to point A; V(A) - V(0) = INTEGRAL(0>a)Edr + INTEGRAL(a>b)E(in)dr + INTEGRAL(b>c)Edr + INTEGRAL(c>A)E(out)dr The first & third integrals are zero, since E = 0 in those regions. The integrals of E(in) & E(out) will give your result. The answer will be logarithmic since you should have found E(in) & E(out) , from Gauss' Law, to be proportional to 1/r . Preliminaries: Coulomb's law that you claim is the only equation you know thus far will not help you, unless you want some painful calculus. We will be using Gauss's law Don't tell me how to approximate Pi. If you are leaving your answer in symbols, leave Pi in symbols too. If you want a numeric value, don't enter Pi's digits, use the pre-programmed value, it is more accurate. --------------------------------- Gauss's law we will use instead: http://hyperphysics.phy-astr.gsu.edu/hba
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