FIGURE P31.38 shows the electric field inside a cylinder of radius $R=3.0$ mm. The field strength is increasing with time as $E=1.0\times {10}^8{t}^2$ V/m, where t is in s. The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for . Find an expression for the electric flux ${\Phi }_e$ through the entire cylinder as a function of time.

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are $E=(200\hat{i}+300\hat{j}-50\hat{k})\text{ V/m}$ and $B=B_0(7.3\hat{i}-7.3\hat{j}+a\hat{k}\mu T$. What is the Poynting vector at this time and position?

A 1.0 μF capacitor is discharged, starting at t = 0 s.The displacement current between the plates is $I_{\text{disp}}=\left(10\text{ A}\right)\exp (-\frac{t}{2.0}\mu \text{s})$. What was the capacitor’s initial voltage (ΔV_C)₀?

A simple series circuit consists of a 150 Ω resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s. Find the electric flux and the displacement current at t = 0.50 ns.

A wire with conductivity σ carries current I. The current is increasing at the rate dI/dt. Evaluate the displacement current for a copper wire in which the current is increasing at 1.0×10⁶ A/s.

A 10 A current is charging a 1.0-cm-diameter parallel-plate capacitor. What is the magnetic field strength at a point 2.0 mm radially from the center of the capacitor?

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are $\overrightarrow{E}=(200\hat{i}+300\hat{j}-50\hat{k})\text{ V/m}$ and $\overrightarrow{B}=B_0(7.3\hat{i}-7.3\hat{j}+a\hat{k})\mu \text{T}$. What are the values of $a$ and $B_0$?