Electric field outside a long cylindrical shell

[MeMoses]

Homework Statement

A long cylindrical shell of radius R = 12.3 cm carries a uniform surface charge 4.60E-6 C/m2. Using Gauss's law find the electrical field at a point p2 = 16.5 from the center of the cylinder.

Homework Equations

EA=q/epsilon0

The Attempt at a Solution

This is what I thought would work but does not produce the answer. The area is arbitrary I believe so I just used a 1m strip of the cylinder, A=2*0.123m*1m=0.246,**2. Q is found by multiplying the area of the cylinder by the charge density, Q=2*pi*r*1*(density)=3.555*10**-6 C. Solve for E, E=Q/(A*epsilon0) =0.163*10**6 N/C which is not correct. Any help would be great, especially if its before 11pm EST tonight.

 

[tiny-tim]

Hi MeMoses!

Difficult to tell without seeing your intermediate steps …

but did you use r = 16.5 ?

 

[MeMoses]

i don't believe r=16.5 is needed, we just need to know that it is outside the cylinder, since it is an infinitely long cylinder the field should not be dramatically affected by distance. I think i just calculated area wrong

 

[tiny-tim]

… since it is an infinitely long cylinder the field should not be dramatically affected by distance.

that works for an infinite flat plate, since the field lines can't get any further apart as they go away …

but they do get further apart from a cylinder, don't they?

 

[netgypsy]

Yup compare the lines for a plane, cylinder/wire and sphere to see how their spacing varies with distance from the object.

 

[MeMoses]

Ok that makes sense now. I feel like an idiot for think that. However, just to clarify, would the equation I need simplify as such, E*A=Q/epsilon -> E(2*pi*r*h)=Q/epsilon, and Q=(2*pi*r*h)*charge density? and would every r here be the distance from the center, not the radius of the cylinder as I previously thought?

 

[MeMoses]

Ok i got, thanks for the help

 

[netgypsy]

Good job!