# Find the electric field at an arbitrary position

1. Oct 28, 2007

### BPBAIR

Problem:

Use Gauss’s Law to find the electric field at an arbitrary position r in the hollow region (ρ =0) between two concentric conducting cylinders. The inner cylinder has radius a and bears a constant charge per unit length, λ, while the outer cylinder has inner radius b and bears the same charge per unit length.

Equation:

Solution:
Not really sure, where to go with this from a geometric point of view.

2. Oct 28, 2007

### siddharth

Ok, first of all, what symmetry can you use in this problem? Is it spherical, cylindrical, etc?

Also, just think of the definition of Gauss' Law, and see where you can apply it here.

3. Oct 30, 2007

### BPBAIR

Well it would have cylindrical symettry. And the field would be completely radial b/c the top and bottom components would cancel leaving only the integral for the sides. rho=0 for in between the two cylinders, which resembles a coaxial cable with a space between the two cylinders. If anyone could help me furtehr on this problem, I would appreciate it. I am confused on how to setup the integrand since it is between two cylinders.

4. Nov 1, 2007

### siddharth

Ok. First of all, you need to construct a hypothetical gaussian surface over which you need to evaluate the surface integral, which in this case will be a cylinder because of the symmetry. First, can you find out what is the elemental area you're integrating over? Can you proceed from here to find the field?

5. Nov 1, 2007

### BPBAIR

figured it out. only the inner cylinder will contribute to the field. from there it is two simple intergrals and the gaussian turns out yo be [ lambda / (2*pi*epsilon*r) ] = E