# Physics

posted by .

A long cylindrical insulator has a uniform charge density of 1.0 #C/m3 and a radius of
9.0 cm.
a) What is the electric field inside the insulator at a distance of 4 cm?
b) What is the electric field at 17 cm?
c) How much work must you do to bring a q = 0.05 #C test charge from 17 cm
to 4 cm?

• Physics -

# means micro

• Physics -

Use Gauss' Law inside and outside the cylinder
a) Inside a uniformly charged cylinder of radius r < 0.09 m, there will be
Q = 10^-6 * pi*r^2*L Coulombs

Gauss' Law says, for this geometry, that
2*pi*r*L*E(r) = Q/epsilon
= 10^-6 * pi*r^2*L
Therefore
E(r) = 10^-6*r/(2*epsilon)
= 2260 Volt/m at r = 0.04 m

For epsilon, I used 8.85*10^-12 C^2/(N*m^2)

(b) Let R = 0.09 m be the solid cylinder radius. r = 17 cm is outside the solid cylinder. The charge inside an outer cylinder of radius r > R is
Q = 10^-6*pi*R^2*L
and the E- field at r > R is again given by Gauss' law
2 pi*r*L*E(r) = 10^-6*pi*R^2*L
E(r) = 10^-6 R^2/(2*r*epsilon)
= 5085*(R/r) Volt/m

c) integrate
(test charge)*E*dr from r = 17 to r = 4 cm. You will have to do in in two parts, inside and outside r = R, since the formulas are different in the two regions.

## Similar Questions

1. ### electrc field inside charged solid

how can electric field exist inside a uniform charge solid... when by gauss law electric field is zero inside a conductor
2. ### Physics-Gauss' Law, hard

Thank you Damon for answering my first questions fast and accurately. Do you or anybody else know how to do these harder Gauss' Law Problems?
3. ### physics

the region 0 < r < r1 is a charged insulating sphere with uniform charge density _E, the region r1 < r < r2 contains free space, and the region r2 < r < r3 is an insulating spherical shell with uniform charge density …
4. ### physics

a thin wire with linear charge density _ is surrounded by a conducting cylindrical shell. (a) If the electric field must be zero inside a conductor, is the electric field due to the wire shielded from extending beyond the conducting …
5. ### Physics

Consider the electric field created by a very long charged line of negative linear charge density -2.50 nC/m. A small positive point charge of 7 mC moves from a distance of 9 cm to a distance of 17 cm. How much work is done by the …
6. ### PHYSICS

A charged disk of radius R that carries a surface charge density ó produces an electric field at a point a perpendicular distance z from the center of the disk, given by: Consider a disk of radius 10 cm and positive surface charge …
7. ### Physics

Consider the electric field created by a very long charged line of negative linear charge density -2.50 nC/m. A small positive point charge of 8 mC moves from a distance of 9 cm to a distance of 17 cm. How much work is done by the …
8. ### physics

Consider the electric field created by a very long charged line of negative linear charge density -2.50 nC/m. A small positive point charge of 12 mC moves from a distance of 7 cm to a distance of 18 cm. In mJ, how much work is done …
9. ### Physic Help

Charge is distributed through an infinitely long cylinder of radius R in such a way that the charge density is proportional to the distance from the central axis: ß = A r, where A is a constant and ß is the density. (a) Calculate …
10. ### Physics

The electric field at a distance of 0.150 m from the surface of a solid insulating sphere with radius 0.367 m is 1720 N/C . Assuming the sphere's charge is uniformly distributed, what is the charge density inside it?

More Similar Questions