Application of Gauss's Law to Charged Insulators

[EngineerHead]

Homework Statement

A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm ra- dially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Use approximate relationships to find (a) the net charge on the shell and (b) the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.

Homework Equations

The Attempt at a Solution

Could someone please explain to me why this does not work:

Flux = Q/e = E*2pi*r*l

Where I am thinking of Q in terms of an average AREA charge density * the area, and not a line density * a length.
-- Is it because it lacks enough independent equations?

 

[Doc Al]

Why do you think that doesn't work?

 

[EngineerHead]

Because I am currently getting a different answer than that given by the book - which is:

+913 nC

 

[EngineerHead]

Okay it works... I've been using an incorrect value for e when solving from k - apologies.

 

[rwisz]

There are a few reasons why this approach may not work:

1. Gauss's Law applies to closed surfaces, not just curved surfaces. In this problem, we are only given information about the electric field at a single point, so it is not possible to use Gauss's Law to directly calculate the net charge on the shell.

2. The formula you are using, Flux = Q/e = E*2pi*r*l, assumes that the electric field is constant over the entire surface. However, in this problem, the electric field is only given at a single point. This formula would only be applicable if the electric field was constant over the entire surface, which is not the case here.

3. The formula you are using, Flux = Q/e = E*2pi*r*l, also assumes that the electric field is perpendicular to the surface at every point. In this problem, we are given the magnitude of the electric field at a point that is not necessarily perpendicular to the surface. In order to use Gauss's Law, we would need to know the direction of the electric field at every point on the surface.

Overall, in order to use Gauss's Law to solve this problem, we would need more information about the electric field on the surface, such as its direction and how it varies over the surface. Without this information, it is not possible to use Gauss's Law to directly calculate the net charge on the shell.