# Why boundary condition in steady electric current?

In summary, boundary conditions are essential in steady electric current as they determine the behavior of the electric field at the boundaries of a system. Dirichlet and Neumann boundary conditions differ in their focus on electric potential and electric field, respectively. These conditions greatly impact the flow of electric current by influencing the distribution of charge and direction of current flow. If boundary conditions are not properly defined, the predictions and models of electric current flow may be inaccurate. Therefore, boundary conditions are necessary for all steady electric current problems in order to fully understand and analyze the behavior of electric current.
when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors

The current density does depend on the electric field strength, but it does not depend only on the electric field strength.

The diagram shows two materials with different conductivities in parallel - if they have the same cross-section, the currents will depend on their conductivities right? That's just the parallel resistors rule.

## 1. Why are boundary conditions important in steady electric current?

Boundary conditions are important in steady electric current because they help determine the behavior of the electric field at the boundaries of a given system. Without proper boundary conditions, it would be difficult to accurately model and predict the flow of electric current in a system.

## 2. What is the difference between Dirichlet and Neumann boundary conditions in steady electric current?

Dirichlet boundary conditions specify the value of the electric potential at the boundary, while Neumann boundary conditions specify the value of the electric field at the boundary. This means that Dirichlet boundary conditions are concerned with the potential difference between two points, while Neumann boundary conditions are concerned with the rate of change of the electric field.

## 3. How do boundary conditions affect the flow of electric current?

Boundary conditions affect the flow of electric current by influencing the behavior of the electric field at the boundaries of a given system. This, in turn, can affect the distribution of charge and the direction of current flow within the system.

## 4. What happens if boundary conditions are not properly defined in steady electric current?

If boundary conditions are not properly defined, the behavior of the electric field at the boundaries of a system may not accurately reflect the physical properties of the system. This can result in inaccurate predictions and models of electric current flow.

## 5. Are boundary conditions necessary for all steady electric current problems?

Yes, boundary conditions are necessary for all steady electric current problems in order to accurately model and predict the behavior of electric current in a given system. Without proper boundary conditions, it is impossible to fully understand and analyze the flow of electric current.

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