Skip to main content

Formula 3. Maxwell equation (differential form) Electric field    Magnetic field

Formula
Formula: 3. Maxwell equation (differential form)

Electric field

Unit
Electric field indicates how large and in what direction the electric force on a charge would be if that charge were placed at location \((x,y,z)\).

In the third Maxwell equation in differential form, on the left-hand side is the rotation \( \nabla \times \class{blue}{\boldsymbol{E}} \) of the electric field, i.e. the cross product between nabla operator \(\nabla\) and E-field. This rotating field corresponds to the negative time derivative of the magnetic field \( \class{violet}{\boldsymbol{B}} \).

Magnetic field

Unit
Magnetic flux density determines the force on a moving electric charge.

The minus sign in front of the time derivative of the magnetic field accounts for the Lenz rule. All in all, the third Maxwell equation states that a magnetic field changing in time causes a rotating electric field and vice versa. It is therefore the law of induction in its general form.