In Ampere's Circuital Law, the missing term refers to the
magnetic field produced by an electric current. The law is typically written as:
\[
\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}}
\]
Where:
- \( \oint \mathbf{B} \cdot d\mathbf{l} \) is the line integral of the magnetic field \( \mathbf{B} \) around a closed loop.
- \( \mu_0 \) is the permeability of free space (a constant).
- \( I_{\text{enc}} \) is the total current enclosed by the loop.
The missing term in Ampere's Law (if you are thinking about adding more general cases, such as displacement current) can be represented by
displacement current in the generalized form (as given by Maxwell's equations):
\[
\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 (I_{\text{enc}} + \epsilon_0 \frac{d\Phi_E}{dt})
\]
Here:
- \( \epsilon_0 \frac{d\Phi_E}{dt} \) represents the displacement current, which accounts for the changing electric field over time.
In the original Ampere's law, the term related to the
displacement current was missing, but Maxwell added it to account for the effects in situations like capacitors where current is not directly flowing but the electric field changes with time.
So, in simple terms, the missing term in the generalized form of Ampere's Circuital Law is
the displacement current term, which represents the changing electric field.