Displacement Current

• Real current:

  • Charge Q passes through area A in time t:

    • $I=\frac{dQ}{dt}$

• Displacement current:

  • Electric flux through area A changes in time

    • $I_D={ϵ}_0\frac{d{\varphi }_e}{dt}$

• These can combine and change Amperes Law into

  • $\oint \vec{B}\cdot d\vec{l}={\mu }_0{ϵ}_0\frac{d}{dt}\int \vec{E}\cdot d\vec{A}$
    • (this combines faraday’s law and Amperes Law)