A very long solid cylinder of radius R = 3 cm has a uniform volume charge densit
ID: 1430278 • Letter: A
Question
A very long solid cylinder of radius R = 3 cm has a uniform volume charge density p = +6 mu C/m^3. Charge: How much total charge is contained on a 1 m length of this cylinder? C What would be the effective linear charge density along the length of this cylinder? Lambda= C/m For a given length of cylinder, what percentage of its total charge lies between 0 and R/2? % Electric Field Outside: What is the electric field at a radial distance of 4 cm from the axis of the cylinder? Inside: What is the electric field at a radial distance of 2 cm from the axis of the cylinder? Now sketch Er vs. r from r=0 to infinity. Mark off where r=R occurs. Inside the cylinder (r smaller than R), graph's shape is: Outside the cylinder (r greater than R), graph's shape is: Voltage Setting V=0 at r=3R, find the voltage at the following locations: Now sketch V vs. r from r=0 to infinity. Mark off where r=R occurs. Inside the cylinder (r smaller than R), graph's shape is: Outside the cylinder (r greater than R), graph's shape is: (Why were you got able to set V=0 at r=infinity in this problem? Is there anything special about setting it at r=3R?)Explanation / Answer
part a.i)
total charge=charge density*volume of the cylinder
=6*10^(-6)*pi*radius^2*length
=6*10^(-6)*pi*0.03^2*1=1.69646*10^(-8) C
part a.ii)linear charge density=total charge/length
=1.69646*10^(-8) C/m
part a.iii)
as volume=pi*radius^2*length
and charge=charge density*volume
charge is proportional to volume as charge density is constant
as volume is prportional to square of radius with length being constant
charge contained is directly proportional to square of radius
hence charge contained in radius R/2=(1/2)^2*total charge
=25% of total charge
part b.i)
as 4 cm > radius of the cylinder,
it will behave like an infinite cylindrical charge with linear charge density=1.69646*10^(-8) C/m
then electric field at a distance of 4 cm=charge density/(2*pi*epsilon*distance)
=1.69646*10^(-8)/(2*pi*8.85*10^(-12)*0.04)=7627.118 N/C