Question

A long coaxial cable consists of an a, b, c,r, A and constants r and ea. charge per unit length A Part B O parailel cylinders axis O radially inward Part C Calculate the magnitude of the electric field at any point autside the outer cylinder a distance r from the axis Express your answer in terms of the variables a, b, e, r, A and constants n and eo. Part D

need part A, part B, part C
part D ask if it is parallel cylinders' axis, radially outward or radially inward
and part E ask to calculate

Answer 1

Solution: (a) IDenTIFy: Apply Gauss's law to a Gaussian cylinder of length / and radius r, where a<r<b, and calculate E on the surface of the cylinder SET UP: The Gaussian suface is sketched in Figure a EXECUTE: ФЕ-E(2tr) encl (the charge on the lengthl of the inner conductor that is inside the Gaussian surface) Figure a λί Og-4nd gives E(2m) encl (b) The enclosed charge is positive so the direction of E is radially outward 0 (c) SET UP: Figure b Apply Gauss's law to a Gaussian cylinder of length / and radius r, where r>c, as shown in EXECUTE: ΦΕ_E(2tr) a = λ1 (the charge on the length 1 of the inner conductor that is inside the Gaussian surface the outer conductor carries no net charge) Figure b λί gives E(277rl)- (d) The enclosed charge is positive so the direction of E is radially outward.

(e) IDENTIFY and SET UP: ier surface: Apply Gauss's law to a Gaussian cylinder with radius r, where b<r<c. We know E on this surface, calculate encl EXECUTE: This surface lies within the conductor of the outer cylinder, where E-0, so фЕ-0. Thus by Gauss's law a 1-0. The surface encloses charge λ/ on the inner conductor. so it must enclose charge -Al on the inner surface of the outer conductor. The charge per unit length on the inner surface of the outer cylinder is iner surface there must be charge per unit length on the outer surface. EvaluaTE: The electric field lines between the conductors originate on the surface charge on the outer surface of the inner conductor and terminate on the surface charges on the inner suface of the outer conductor These surface charges are equal in magnitude (per unit length) and opposite in sign. The electric field lines outside the outer conductor originate from the suface charge on the outer suface of the outer conductor