- #1
zelscore
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- Homework Statement
- Figure 2.29 depicts a long cylindrical charge with a radius a placed in free space
of permittivity e. A charge Q per unit length is uniformly distributed within a
circular cylinder. Determine the electric field.
Hint: Construct a cylindrical Gaussian surface surrounding the charge and apply
Gauss’s law.
Fig 2.29 is basically just a cylinder on a z-axis and where the radius is described as p=a, with the letter Q inside the cylinder
- Relevant Equations
- From wikipedia https://en.wikipedia.org/wiki/Gaussian_surface#Cylindrical_surface
Q = yh, where y is the charge density, and h is the length of the cylinder
Flux of electric field E is the sum of all surface flux
Gauss law: Flux = Q/e
I begin by calculating the flux to be the flux of the cylinders lateral surface, which equals E*2*pi*p*h (p is the radius)
The other two surfaces have E ortogonal to dA, so their flux is 0.
Using Gauss law together with the calculated flux above, I get
Flux = Q/e
Flux = E*2*pi*p*h
Solve for E
E*2*pi*p*h = Q/e
E = Q/2*pi*e*p*h
Q = yh, so
E = y/2*pi*e*p for p >= a which is the same result as wikipedia gets, and this website too http://www.ncert.nic.in/html/learni...city/electrostatics/ef_cylinder_of_charge.htm
using Q instead of y:
E = Q/2*pi*e*p*h for p >= a
HOWEVER, the book I use get
E = Q/2*pi*e*p for p >= a
Which leads me to believe that, in Q = yh, and where h is the length of our "long" cylinder, h can be set to 1 and thus Q = y?
This is my first time posting so if I didn't follow the rules somehow please do tell.
The other two surfaces have E ortogonal to dA, so their flux is 0.
Using Gauss law together with the calculated flux above, I get
Flux = Q/e
Flux = E*2*pi*p*h
Solve for E
E*2*pi*p*h = Q/e
E = Q/2*pi*e*p*h
Q = yh, so
E = y/2*pi*e*p for p >= a which is the same result as wikipedia gets, and this website too http://www.ncert.nic.in/html/learni...city/electrostatics/ef_cylinder_of_charge.htm
using Q instead of y:
E = Q/2*pi*e*p*h for p >= a
HOWEVER, the book I use get
E = Q/2*pi*e*p for p >= a
Which leads me to believe that, in Q = yh, and where h is the length of our "long" cylinder, h can be set to 1 and thus Q = y?
This is my first time posting so if I didn't follow the rules somehow please do tell.