EM Fundamentals > Mathematical notions

Step 1/6

Glossary

Step 2/6

Linear Operators

Step 3/6

Linear operators in action - Gradient of the electric field amplitude

Step 4/6

Linear operators in action - Divergence of the electric field amplitude gradient

Step 5/6

Linear operators in action - Curl of the magnetic field

Step 6/6

Handy Identities and Theorems

Step 1: Glossary
To avoid confusions between physical quantities, a glossary must be defined.

Step 2: Linear Operators
Physical meaning of some linear operators helps with EM theory understanding.

Step 3: Linear operators in action - Gradient of the electric field amplitude
Two opposite electric charges are used to create an electric dipole in a homogeneous medium. Electric field amplitude is shown with colored contours. Its respective color bar appears on the right-hand side. Electric field lines are displayed as black lines and correspond to the Electric field amplitude gradient.

Step 4: Linear operators in action - Divergence of the electric field amplitude gradient
Several electric charges are randomly distributed in a homogeneous medium. Electric field lines correspond to the gradient of the Electric field amplitude like in Step 3. Color-coded information is the divergence of the Electric field amplitude gradient. Its respective color bar appears on the right-hand side.

Step 5: Linear operators in action - Curl of the magnetic field
The image plane is considered perpendicular to infinite wires flowed by an electric current. Color-coded information is the curl of the Magnetic field induced by current flows. Its respective color bar appears on the right-hand side. Magnetic vector field is displayed with black arrows.

Step 6: Handy Identities and Theorems
Handy identities and Theorems are reminded to discuss further issues.