I am working on Metamaterials and getting more information about it. Regarding that, I want to know what does it mean exactly that tangential component of E (Electric) is Zero. Please Help
If an EM wave is directly incident (at 0 degrees incident angle) to a surface, the component of the E-field which points away from the surface (i.e. the direction which defines the orientation of the plane of incidence) will be zero.
However, if the wave has a non-zero incidence angle with the surface, there will be a component of the E-field which points in the direction normal to the incidence plane.
Therefore, saying that the tangential component of the E-field is zero is equivalent to saying the angle of incidence (in the plane containing the E-field vectors) is zero.
If the tangential component of the B-field is also zero, then the wave is exactly perpendicular to the surface.
My previous answer is wrong. Paragraphs 1&2 are correct but I'm talking about the normal component, not the tangential component. I work with waveguides and the tangential component to a guide interface is parallel to the guide input facet normal. I got confused in my thought process.
The tangential component means a variety of things unfortunately and probably explains the lack of clarity between available explanations. The tangential component is tangent to the surface, so any vector that is perpendicular to the normal of the surface can be considered a tangential component. If a tangential component of the Efield is zero, then essentially you can say that the wave is polarised at 90 degrees to this tangential vector in normal incidence conditions.
You need to first clarify whether you are talking about the electrostatic E field as per Gauss's Law, or the oscillating E field that arises in electromagnetic radiation. The former is radial and has no tangential component. As regards the latter, you first need to set up a physical model and figure out where your polar origin will be placed. In the mathematical analysis of EM radiation, the divergence of E has to be zero, implying that in this case E is tangential to the polar origin.
When the tangential component of the electric field is zero, this is the boundary condition associated with a material that is perfectly electrically conducting (PEC). The electric field here is the total electric field - the incident field plus the scattered field. Metallic layers can usually be treated as PEC materials over a wide range of frequencies of electromagnetic waves. The other case where you might encounter a zero tangential electric field is where interfering waves produce a particular plane of symmetry on which the tangential E field is zero. Such surfaces are sometimes referred to as 'electric walls' and are often exploited in computational electromagnetics codes as a way to reduce the size of a computational task (by using symmetry). For a surface with normal unit vector n, the tangential electric field can be expressed as the vector product n x E where E is the total electric field vector. Hope this helps.
The line integral of E field between any two points give the voltage drop. Now suppose, If we have an E field tangential component outside a PEC, we will have a tangential component of field inside the conductor as well. The inside component will give rise to voltage drop but we know a perfect electric conductor has infinite conductivity, therefore we expect the voltage drop must be zero inside the conductor. To have this, the tangential component of E field has to be zero. It should be normal. Hope it answers the question.
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