In Maxwells equations, the displacement current is included to:
A. Account for the magnetic field generated by a moving charge.
B. Modify Gauss’s law for electricity.
C. Ensure the continuity of current in Ampere’s law.
D. Describe the electric field in a vacuum.
The correct answer and explanation is:
The correct answer is C. Ensure the continuity of current in Ampere’s law.
Maxwell’s equations describe the behavior of electric and magnetic fields and their interactions with matter. One of the key modifications that Maxwell made to Ampere’s law was the introduction of the displacement current. This was needed to ensure the continuity of current and to account for situations where electric fields change over time, such as in capacitors.
In classical electromagnetism, Ampere’s law describes how a magnetic field is generated by a current-carrying conductor. It states that the magnetic field around a conductor is proportional to the current flowing through it. However, Ampere’s law, in its original form, fails in situations where there is a time-varying electric field but no actual current (for example, between the plates of a charging capacitor).
To address this, Maxwell introduced the concept of the displacement current. The displacement current is a term that appears in the modified form of Ampere’s law and is proportional to the rate of change of the electric field in a region. By adding this term, Maxwell ensured that the law holds true even in regions where there are no physical charges in motion, but the electric field is changing with time.
The displacement current accounts for the changing electric fields that can create a magnetic field, even in the absence of physical currents. This was crucial in explaining phenomena such as electromagnetic waves, where oscillating electric and magnetic fields propagate through space without the need for physical charges.
This modification also led to the unification of the electric and magnetic fields into a single theory of electromagnetism, laying the groundwork for the development of modern physics.