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## 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!

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