Using Gauss\'s Law find the electric field inside and outside a\"non-conducting\

Question

Using Gauss's Law find the electric field inside and outside a"non-conducting", uniformly charged cylinder with radius 10 cm. andcharge density 16 uC/m^2?(Treat the cylinder as it is verylong) B) Calculate the potential difference at a distance of 20 cmfrom the center of the cylinder to a distance of 5 cm from thecenter. I do not at all how to approach to this problem. Using Gauss's Law find the electric field inside and outside a"non-conducting", uniformly charged cylinder with radius 10 cm. andcharge density 16 uC/m^2?(Treat the cylinder as it is verylong) B) Calculate the potential difference at a distance of 20 cmfrom the center of the cylinder to a distance of 5 cm from thecenter. I do not at all how to approach to this problem.

Explanation / Answer

The problem does not specify whether the cylinder is solid orhollow. Since charge density () is given in terms ofm2 one must assume the cylinder to be hollow. = Q / 0 where Q is the charge enclosedby a Gaussian cylinder Q = 2 Rc L where Rcis the radius of the charge carrying cylinder A = 2 RG L where RG is theradius of a Gaussian surface = E A = Q / 0 and E = Q /(0 A) = 2 Rc L /( 2 RG L) = Rc /RG There is no electric field within the cylinder and hence thepotential is constant within the cylinder So integrate E from .2 m to .1 m to get the required potentialdifference Rc integral d RG /RG = Rc ln RG =Rc ln (.1 / .2) = 1.43  Rc There is no electric field within the cylinder and hence thepotential is constant within the cylinder So integrate E from .2 m to .1 m to get the required potentialdifference Rc integral d RG /RG = Rc ln RG =Rc ln (.1 / .2) = 1.43  Rc

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