16.1 Maxwell’s Equations and Electromagnetic Waves

When the emf across a capacitor is turned on and the capacitor is allowed to charge, when does the magnetic field induced by the displacement current have the greatest magnitude?

Could a purely electric field propagate as a wave through a vacuum without a magnetic field? Justify your answer.

Explain how the displacement current maintains the continuity of current in a circuit containing a capacitor.

Why is it much easier to demonstrate in a student lab that a changing magnetic field induces an electric field than it is to demonstrate that a changing electric field produces a magnetic field?

Show that the magnetic field at a distance r from the axis of two circular parallel plates, produced by placing charge Q(t) on the plates is
$B_{\text{ind}} = \frac{\mu_{0}}{2 \pi r} \frac{d Q \left(t\right)}{d t}$.

A potential difference $V \left(t\right) = V_{0} \text{sin} \omega t$ is maintained across a parallel-plate capacitor with capacitance C consisting of two circular parallel plates. A thin wire with resistance R connects the centers of the two plates, allowing charge to leak between plates while they are charging.
(a) Obtain expressions for the leakage current $I_{\text{res}} \left(t\right)$ in the thin wire. Use these results to obtain an expression for the current $I_{\text{real}} \left(t\right)$ in…

The potential difference V(t) between parallel plates shown above is instantaneously increasing at a rate of $10^{7} \text{V}/\text{s} .$ What is the displacement current between the plates if the separation of the plates is 1.00 cm and they have an area of $0.200 \left( \text{m}\right)^{2}$ ?

The voltage across a parallel-plate capacitor with area $A = 800 \left( \text{cm}\right)^{2}$ and separation $d = 2 \text{mm}$ varies sinusoidally as $V = \left(15 \text{mV}\right) \text{cos} \left(150 t\right)$, where t is in seconds. Find the displacement current between the plates.