Conductors in Electrostatic Equilibrium

In summary, the electric field x cm away from a long straight metal rod with a radius of 5 cm and a charge per unit length of 30 nC/m can be found using the equation ## \int E\cdot dA = \dfrac{q_{encl}}{\epsilon_0}##. This is because the rod, being infinite, is enclosed by a closed gaussian surface. If x < 5, a gaussian cylinder with a radius of x can be used, and the equation can be simplified by pulling out the constant electric field and using the area of the cylinder, ##2\pi x l##, as the enclosed area. The "caps" of the cylinder can be ignored since the rod is infinite
  • #1
oneplusone
127
2
A long straight metal rod has a radius of 5 cm and a charge per unit length of 30 nC/m. Find the electric field x cm away where distance is perpendicular to the rod.The solution to this uses ## \int E\cdot dA = \dfrac{q_{encl}}{\epsilon_0}##. My question is, why can you use this? I thought that is only when the gaussian surface is closed.

I understand the rest of the solution, but this theoretical part is confusing me…

thanks :smile:
 
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  • #2
My first thought; The rod is "long" which is a buzz word for infinite. An infinite road is enclosed by an area, the area of the gaussian cylinder that surrounds it. There are no endcaps because the rod is infinite so the area is closed.
 
  • #3
Hmmm, so suppose that x < 5 (find field inside rod)…
does that mean you construct a gaussian cylinder that has radius x? And then use the equation above?

And since it is infinite, am I correct in saying that we can pull ##E## out of the integral (it is constant), and ##A## would just be ##2\pi x l## (we can ignore the "caps" of the cylinder since it's infinite?)
 

FAQ: Conductors in Electrostatic Equilibrium

1. What is electrostatic equilibrium?

Electrostatic equilibrium is a state in which the net electric charge on a conductor is zero and the electric field inside the conductor is zero. This means that the charges on the surface of the conductor are evenly distributed and there is no movement of charges.

2. What is a conductor?

A conductor is a material that allows electric charges to flow freely through it. In the context of electrostatic equilibrium, a conductor is a material that can achieve a state of zero net charge and zero electric field inside when placed in an electric field.

3. How does a conductor achieve electrostatic equilibrium?

A conductor achieves electrostatic equilibrium by allowing charges to move freely until they are evenly distributed on its surface. This process is known as electrostatic induction. The free movement of charges is possible due to the high electrical conductivity of the material.

4. What are some examples of conductors in electrostatic equilibrium?

Some examples of conductors in electrostatic equilibrium include metal objects such as copper wires, aluminum foil, and metal spheres. These objects are able to achieve electrostatic equilibrium due to their high electrical conductivity.

5. How does the shape of a conductor affect electrostatic equilibrium?

The shape of a conductor can affect electrostatic equilibrium by influencing the distribution of charges on its surface. For example, a pointed conductor will have a higher charge density at its tip compared to a flat conductor, as the electric field is stronger at sharper points.

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