# Current density and vector potential

• oddiseas
In summary, the question asks for the current density needed to produce a given vector potential in cylindrical coordinates. The attempt at a solution involved using the equation B=grad*A, but due to a mistake in the formula, the resulting current density was zero. A hint was given to fix the error.
oddiseas

## Homework Statement

What current density would produce the vector potential
A(r)=(-kmu/2pi)In(r/a) (in the z direction)

where k is a constant, in cylindrical coordinates?

## The Attempt at a Solution

i have done this three times and i get zero current density.So i am wondering if i am making a mistake, there is only one component for A the z component so when i use B=grad*A, i get a field in the fita direction, then when i use J=(grad*B)/mu i get zero.

oddiseas said:

## Homework Statement

What current density would produce the vector potential
A(r)=(-kmu/2pi)In(r/a) (in the z direction)

where k is a constant, in cylindrical coordinates?

## The Attempt at a Solution

i have done this three times and i get zero current density.So i am wondering if i am making a mistake, there is only one component for A the z component so when i use B=grad*A, i get a field in the fita direction, then when i use J=(grad*B)/mu i get zero.

Hint: $\frac{r}{r}$ is undefined at $r=0$

## 1. What is current density?

Current density is a physical quantity that describes the flow of electric charge in a given material or medium. It is a vector field that represents the amount of electric current passing through a unit area per unit time.

## 2. How is current density related to electric current?

Current density and electric current are closely related, as current density is the amount of electric current passing through a unit area. The total electric current passing through a surface can be calculated by integrating the current density over that surface.

## 3. What is vector potential?

Vector potential is a mathematical vector field that is used to describe the magnetic field in a given space. It is related to the magnetic vector potential, which is defined as the curl of the vector potential. Vector potential is used in Maxwell's equations to describe the behavior of electromagnetic fields.

## 4. What is the relationship between current density and vector potential?

Current density and vector potential are closely related through Maxwell's equations. The vector potential is used to calculate the magnetic field, which in turn is related to the current density through Ampere's law. In other words, the vector potential is a crucial component in understanding the behavior of current density and electromagnetic fields.

## 5. How is current density and vector potential used in practical applications?

Current density and vector potential have many practical applications in various fields, such as electrical engineering, physics, and material science. They are used to model and understand the behavior of electric and magnetic fields, which is essential for designing and optimizing devices such as motors, generators, and transformers. They are also used in medical imaging techniques such as magnetic resonance imaging (MRI).

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