# Cylinderical reigon and potential difference

• fight_club_alum
In summary, to find the potential difference between points A and B, we can use the equation -integral(E . dr) = delta V, where E is the electric field and dr is the distance between the points. Using the given information, we can calculate the electric field at point A using the formula EA = Q/eo, where Q is the charge and eo is the permittivity of free space. Then, we can use the formula E = (lambda) /( eo * 2 * pi * r) to find the electric field at point B, where lambda is the charge density and r is the distance from the symmetry axis. Finally, plugging these values into the integral and solving, we get a potential difference of
fight_club_alum

## Homework Statement

The charge of density 3.0 μC/m fills a long cylindrical region having a 2.0-cm radius. If point A is 1.0 cm from the symmetry-axis and point B is 2.0 cm from the symmetry-axis, what is the potential difference VA – VB?
a . –25 mV

b. +42 mV

c. –42 mV

d. +25 mV

## Homework Equations

- integral( E . dr) = delta V

## The Attempt at a Solution

EA = Q/eo
E(2*pi*r*h) = lambda * h / eo
E = (lambda) /( eo * 2 * pi * r)
-integral(lambda/eo* 2 * r * pi) dr from 0.01 ro 0.02 <--- gives me the wrong answer

yes. did you notice A is 'inside' the charge ?

## What is a cylindrical region and how is it different from a spherical region?

A cylindrical region is a three-dimensional shape that is formed by extending a two-dimensional circle along its central axis. It is different from a spherical region, which is formed by extending a two-dimensional circle in all directions, as a cylindrical region has a flat base and top, while a spherical region has a curved surface.

## What is potential difference and how is it measured in a cylindrical region?

Potential difference, also known as voltage, is the difference in electric potential between two points in an electric field. In a cylindrical region, potential difference is measured by the ratio of the change in electric potential to the distance between the two points.

## How does the size of a cylindrical region affect the potential difference?

The size of a cylindrical region does not affect the potential difference, as long as the distance between the two points remains the same. However, a larger cylindrical region may have a larger capacitance, which can affect the amount of charge stored and therefore the potential difference.

## What is the relationship between electric field and potential difference in a cylindrical region?

In a cylindrical region, the electric field is directly proportional to the potential difference. This means that if the potential difference increases, the electric field will also increase proportionally.

## How is the potential difference distributed in a cylindrical region with a uniform electric field?

In a cylindrical region with a uniform electric field, the potential difference is distributed evenly along the length of the cylinder. This means that the potential difference between any two points on the cylinder will be the same, regardless of their distance from the center or the base.

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