Question

L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown below, (). State the Gauss's law for electric field in words. [1) (i). In order to calculate the electric field inside the cylinder using Gauss's Law, draw an appropriate Gaussian surface in the cylinder. [1] (i). Use the above information or otherwise, show that the electric field in the radial direction Pt inside the cylinder is ,2a (assume that the charge is evenly distributed inside the eylinder). 12] (iv). In order to calculate the electric field outside the cylinder surface using Gauss's Law, draw an appropriate Gauss's surface around the cylinder [1] (v). Use the above information or otherwise, find an expression for the electric field outside the cylinder. [2) (vi). Plot the magnitude of radial electric field E, with respect to the radial component r inside and outside the cylinder, with E field strength at r a indicated in the plot [2] (vi). Use the potential difference equation to show that the expression for potential difference -In 2, a outside the cylinder (Vr)-Vla) for r> a) is equal to- (viii). Find an expression for an absolute potential Pat the cylinder surface, r- a, or Ma), assuming that potential P at a large distance h. (r-h a), Vh)-0.[1 (ix). Use the potential difference equation to show that the expression for potential difference inside Pir the cylinder (Wr)-VO), for r< a) is equal to - 4 (2) (x). Plot the electric potential Vr) with respect to the radial componet r, indicating the points Vh), Ma) and の. [3] (xi). If the cylinder material is now a conductor (ie., copper wire), plot a new potential Vr) function. [2] (xii), Use the above information or otherwise, calculate the electric field inside a conducting cylinder [2] (b) A long, conducting high-voltage line is supported a distance h 10 m above the ground. The ground can be treated as an ideal conducting plane at zero potential. The radius of the circular cross-section of the line is a I cm ha In the vertical (XY) plane containing the wire, in the region 0<y<h-a, the electric field is given approximately by: P E,(xy0)-2h-y h+y :0<ych-a where p is the lincar charge density on the wire Briefly explain the concept of mirror image of a charge on a conducting surface. [2) (0. Briefly explain why there are two terms in this expression and why they depend on the distances from the wire as shown in the equation. (You may assume that the radius of the wire is sufficiently small that the wire can be approximated by a line charge on its axis.) [3 (i) Show that the potential difference between the surface of the wire and the ground plane is of the form: [5) (i). 24 PIn 2m,

Answer 1

caytindes length f the the CAven chage density aciizus a Line and iOKEd flux The Electoi elds:- Gauss law foo he by thoough suofate given Suslace by the by chasge Enclosed Es Cin vacuum) mathe mahically enclesed su slace Gcussian Gaussian susface and defiaition using above Soom denclosed lat faces fespenckulax Cade thei& dot pduct dentlod E . 2

total chasge the be chosye Enclered T 32 -A a1 TTa => the flux dinKs suslace this Since