The component of the electric field intensity that is always continuous at the boundary is the tangential component.

Electric field intensity is a vector quantity that describes the strength and direction of an electric field at a point in space. When an electric field encounters a boundary between two different mediums, such as air and a dielectric material, the electric field can change.

Boundary conditions for electric fields

Boundary conditions are mathematical relationships that describe how the electric field behaves at the boundary between two different mediums. These conditions help us understand how the electric field changes when it encounters a boundary.

There are two main boundary conditions for electric fields:

1. Tangential component continuity: The tangential component of the electric field must be continuous across a boundary. This means that the tangential component of the electric field on one side of the boundary must be equal to the tangential component on the other side of the boundary.

2. Normal component discontinuity: The normal component of the electric field can have a discontinuity across a boundary. This means that the normal component of the electric field on one side of the boundary may not be equal to the normal component on the other side of the boundary.

Explanation of why the tangential component is always continuous:

The tangential component of the electric field is parallel to the boundary and is responsible for the flow of charge along the surface of the boundary. This component must be continuous because the charge distribution on the boundary cannot abruptly change.

If the tangential component of the electric field were not continuous at the boundary, there would be a sudden jump in the charge density along the surface, which is physically not possible. Therefore, the tangential component of the electric field must remain continuous to ensure the smooth flow of charge along the boundary.

In contrast, the normal component of the electric field can have a discontinuity because it is responsible for the flow of charge across the boundary. The normal component can change when crossing the boundary between two different mediums, as the charge distribution and permittivity of the mediums may vary.

Conclusion:

In summary, the tangential component of the electric field is always continuous at the boundary between two different mediums. This is because the charge distribution along the boundary cannot abruptly change, and the tangential component is responsible for the flow of charge along the surface. In contrast, the normal component of the electric field can have a discontinuity across the boundary.