- #1
orb123
- 3
- 0
Homework Statement
A long cylindrical insulator has a uniform charge density of 0.94 µC/m³, and a radius of 7cm (R). Find the electric field inside the insulator at a adistance of 4cm (r). Answer in units of N/C.
Homework Equations
Variables:
q= charge in the gaussian surface
R= Radius of cylinder
r= radius of gaussian surface of cylinder ; r<R
L= Lenght of gaussian surface of cylinder
Equations:
EA=q/ε0
V= (pi)R²L
V'= (pi)r²L
q=pV' volume of the gaussian surface of the cylinder
Q=pV; Q= charge, p=charge density
A=2(pi)RL = Area of cylinder (only the curved surface)
The Attempt at a Solution
Ok, I'm solving the gaussian surface of the cylinder. I know q<Q, and q=pV' = p{(pi)r²L}.
Then, I know p=Q/V by definition, so q=Q{(pi)r²L}/V.
Pluggin it into the first equation:
EA = Q{(pi)r²L}/{V(ε0)}
E{2(pi)RL}=Q{(pi)r²L}/{V(ε0)}
Solving:
E= Qr²/{2V(ε0)R} ; Then replacing V
E= Qr²/{2(pi)R²L(ε0)R} (??)
Why do I still have L there? I was not given a value for that, and it was supposed to be eliminated during solving the equations. And even if L wasn't there, the final solution would not be in units of N/C. What am I doing wrong?
Thanks!
Last edited: