General question pertaining to a thin rod and E

In summary, the conversation discusses the calculation of electric potential at two points, P1 and P2, on the z-axis and x-axis respectively, due to a uniformly charged thin rod extending from z = -d to z = d with linear charge density lambda. The potential at P1 is found to be lambda ln(3) by integrating over the charge distribution, and the potential at P2 is calculated by setting it equal to the potential at P1 and integrating from d to d+2d. The conversation also mentions confusion over whether the potential difference or potential energy is being calculated, and the use of the formula lambda/r for an arbitrary length of wire.
  • #1
enkerecz
11
0
I was under the assumption that the electric field for an arbitrary length of wire was 2[tex]\lambda[/tex]/r.

In this problem

A thin rod extends along the z-axis from z = -d to z = d. The rod carries a charge
uniformly distributed along its length with linear charge density lamda. By integrating over
this charge distribution, calculate the potential at a point P1 on the z-axis with coordinates (0,0,2d). By another integration find the potential at a point P2 on the x-axis and locate this point to make the potential equal to the potential at P1.

The potential at (0,0,2d) is [tex]\lambda[/tex] ln(3)...

Of course, the potential is the integral of E[tex]\bullet[/tex]ds

the second part follows naturally from the first, so I'm not concerned with it.

Am I missing something here? Do that want potential difference or potential energy? I'm assuming it is electric potential difference, but their methods confuse me.. The book completely ignores the formula it gave for a wire and decided the answer to this was only the integral of (lamda/r) dr from point d to d+2d... How can they just drop off a scalar like that?
 
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  • #2
Lambda = charge/length;

[tex]\lambda[/tex]r/r^2=E=[tex]\lambda[/tex]/r
I feel like a complete idiot for struggling with this for so long..
 

1. What is a thin rod and how is it different from a thick rod?

A thin rod is a long, slender object with a small diameter compared to its length. It is different from a thick rod in that it has a smaller cross-sectional area and is more likely to bend or deform under stress.

2. What are some common applications of thin rods?

Thin rods are commonly used in construction, engineering, and manufacturing industries for various purposes such as support structures, tension members, and electrical wiring.

3. How does the thickness of a rod affect its strength?

The thickness of a rod can significantly impact its strength. Generally, a thicker rod will be stronger and able to withstand higher forces without bending or breaking. However, the material and composition of the rod also play a significant role in determining its strength.

4. How is the strength of a thin rod calculated?

The strength of a thin rod is calculated using the equation E = (M * L) / (R * A), where E is the Young's modulus, M is the bending moment, L is the length of the rod, R is the radius of the rod, and A is the cross-sectional area. This equation takes into account both the material properties and the dimensions of the rod.

5. Can a thin rod be considered infinitely rigid?

No, a thin rod can never be considered infinitely rigid as it will always have some degree of flexibility and deform under stress. However, the degree of rigidity can vary based on the material and dimensions of the rod.

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