# Electric Potential: Q, a, b, Vb & Va

In summary, the problem involves a coaxial line with two perfect conductors, one with radius a and the other with radius b, where the outer conductor is grounded. The inner conductor has a charge density of 1[C/m]. The potential difference between the two conductors can be found using the formula V= (Q/4*pi* ε0)( 1/a-1/b), where Q is the unknown charge. The potential of the outer conductor is 0[V], and the potential of the inner conductor is (Q/4*pi*ε0)(1/a). To find Q, the charge density must be calculated using the formula \rho = \frac {1 Coulomb} {2 \pi a meter^2}.
Hi,
I would like to have some guidance with this problem. i would like to know please, if I do good or bad.

A coaxial line is made of two perfect conductors. The inner cylinder has radius a and the radius of the outer one is b. The outer conductor is grounded.
Suppose that the inner conductor carries 1[C] of charge per meter of its length, that is its equivalent line charge density is ρlo=1[C/m].

a- Find the potential difference between the two conductors.
b- What is the potential of the outer conductor?
c- What is the potential of the inner conductor?

a-
V= (Q/4*pi* ε0)( 1/a-1/b)

with Q=?

b-
Vb=0[V]

c-

Va=(Q/4*pi*ε0)(1/a)

I have some issue with the value of Q. since the length is not specified should Q be Q=1*L=L (Length)??

The trick here is to figure out the charge density which is :

$$\rho = \frac {1 Coulomb} {2 \pi a meter^2}$$

You have to divide the C/meter by the distance around which of course is a $$2 a \pi$$ meter. That gives you the charge density on the surface.

Given the density, you can solve for the electrical field which is what you were close to doing in your answer in part a.

That isn't quite right since the electric field has a direction, but that can be ignored in this problem if we assume everything is along the radial direction.

The only problem is that isn't the potential. You need to integrate the negative the distance from b to a to get the potential.

Last edited:
Does anyone know what the correct solutions are to this problem?

## 1. What is electric potential?

Electric potential is the amount of potential energy per unit charge at a given point in an electric field. It is a measure of the ability of an electric field to do work on an electric charge.

## 2. How is electric potential represented?

Electric potential is often represented by the symbol V and is measured in units of volts (V). It can also be represented by the letters Phi or U.

## 3. What is the relationship between electric potential and electric field?

Electric potential and electric field are closely related. Electric potential is the potential energy per unit charge while electric field is the force per unit charge. The electric field is the negative gradient of the electric potential.

## 4. What is the difference between electric potential and electric potential energy?

Electric potential is a measure of the potential energy per unit charge at a given point in an electric field. Electric potential energy, on the other hand, is the potential energy that a charged particle possesses due to its position in an electric field.

## 5. How are Q, a, b, Vb, and Va related in electric potential?

Q, a, b, Vb, and Va are all related in the formula for electric potential. Q represents the charge, a and b represent two points in an electric field, Vb is the electric potential at point b, and Va is the electric potential at point a. The formula for electric potential is Vb - Va = kQ(b-a)/r, where k is a constant and r is the distance between points a and b.

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