16.1 Maxwell’s equations and electromagnetic waves  (Page 6/8)

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

Describe the field lines of the induced magnetic field along the edge of the imaginary horizontal cylinder shown below if the cylinder is in a spatially uniform electric field that is horizontal, pointing to the right, and increasing in magnitude.

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
$B_{\text{ind}}=\frac{{\mu }_0}{2\pi r}\frac{dQ\left(t\right)}{dt}$ .

Express the displacement current in a capacitor in terms of the capacitance and the rate of change of the voltage across the capacitor.

A potential difference $V(t)=V_0\text{sin}\omega t$ 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 wires connected to the capacitor.
(b) Find the displacement current in the space between the plates from the changing electric field between the plates.
(c) Compare $I_{\text{real}}\left(t\right)$ with the sum of the displacement current $I_{\text{d}}\left(t\right)$ and resistor current $I_{\text{res}}\left(t\right)$ between the plates, and explain why the relationship you observe would be expected.

Suppose the parallel-plate capacitor shown below is accumulating charge at a rate of 0.010 C/s. What is the induced magnetic field at a distance of 10 cm from the capacitator?

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

A parallel-plate capacitor has a plate area of $A=0.250{\text{m}}^2$ and a separation of 0.0100 m. What must be must be the angular frequency $\omega$ for a voltage $V\left(t\right)=V_0\text{sin}\omega t$ with $V_0=100\text{V}$ to produce a maximum displacement induced current of 1.00 A between the plates?

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

The voltage across a parallel-plate capacitor with area A and separation d varies with time t as $V=a{t}^2$ , where a is a constant. Find the displacement current between the plates.