# Potential for two semicircular rods

• phantom113
In summary, the problem involves two semicircular rods of different radii joined by two straight rods, with a charge of lambda coulombs per meter. The goal is to calculate the potential at point p, located at the center of the concentric circles formed by the two semicircles. The equations used for this calculation are V= KQ/R and V= E*s. The main question is whether the electric field between the two rods cancels out, leaving only the electric field due to the inner rod, and if so, does the integral for finding the potential go from 0 to R1?
phantom113

## Homework Statement

Two semicircular rods, one of radius R1 and the other of radius R2 where R2 > R1, are joined by two horizontal, straight rods. The rods carry a charge of lambda coulombs per meter. Calculate the potential at point p at the center of the two semicircles. (P would be the center of the two concentric circles if the rods were full circles)

This configuration looks like a rainbow basically and p is on the ground halfway between each side of the rainbow.

V= KQ/R
V= E*s

## The Attempt at a Solution

If I calculate V using the electric field, does the electric field between the two rods cancel so I would just have to use the electric field due to the inner rod? I know the electric fields of the two horizontal rods cancel.

Anyone?

OK I suppose my real question is, is the electric field at point P

2k(lambda)*(1/R1 + 1/R2)

And then if that is so, to find the potential does the integral go from 0 to R1?

## 1. What is the potential of two semicircular rods?

The potential of two semicircular rods refers to the electric potential energy between them. It is a measure of the work required to move a unit of charge from one rod to the other, and is affected by the distance and charge distribution of the rods.

## 2. How is the potential between two semicircular rods calculated?

The potential between two semicircular rods can be calculated using the formula V = kQ/r, where k is the Coulomb's constant, Q is the charge of each rod, and r is the distance between the rods.

## 3. What factors affect the potential between two semicircular rods?

The potential between two semicircular rods is affected by the distance between the rods, the charge of each rod, and the shape and distribution of the charge on the rods.

## 4. Can the potential between two semicircular rods be negative?

Yes, the potential between two semicircular rods can be negative depending on the charge distribution and distances between the rods. A negative potential indicates that work must be done to move a unit of charge from one rod to the other, and that the rods are repelling each other.

## 5. How does the potential change if the distance between two semicircular rods is increased?

If the distance between two semicircular rods is increased, the potential between them decreases. This is because the force between the rods decreases as the distance increases, resulting in a lower potential energy between the rods.

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