Question

A thin cylindrical shell of radius R1=5.0cmR1=5.0cm is surrounded by a second cylindrical shell of radius R2=8.0cmR2=8.0cm, as in the figure (Figure 1). Both cylinders are 9.0 mm long and the inner one carries a total charge Q1=−0.71μCQ1=−0.71μC and the outer one Q2=+1.56μCQ2=+1.56μC.

A) For points far from the ends of the cylinders, determine the magnitude of the electric field at a radial distance r from the central axis of 5.9 cm.  

B) For points far from the ends of the cylinders, determine the magnitude of the electric field at a radial distance r from the central axis of 12.5 cm .

Answer 1

(A) Let's assume a gaussian cylndrical surface of radius r = 5.9 cm and length l. This cylinder is coaxial with the other two cylinders given in the question.

Electric flux through it's sides is

Charge inside is,

Using Gauss' Law,

(B) This time, assume a gaussian surface of r = 12.5 cm

From part (A)