Maxwell’s equations and electromagnetic waves

The uniform electric field between the plates of a parallel-plate capacitor in vacuum, of area $A=0.040{\mathrm{m}}^2$, grows at the rate $\frac{dE}{dt}=5.0\cdot 10^{11}V/(\mathrm{m}\cdot \mathrm{s})$. Neglecting edge effects, compute the displacement current between the plates.

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A capacitor of capacitance $C=4.0\mathrm{nF}$ is charged with a current $i=1.5\mathrm{mA}$. Compute the displacement current between the plates and the rate at which the potential difference grows.

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A parallel-plate capacitor in vacuum with circular plates of radius $R=6.0\mathrm{cm}$ is charged with current $i=3.0\mathrm{A}$. Neglecting edge effects, compute the magnitude of the magnetic field between the plates at distance $r=3.0\mathrm{cm}$ from the axis.

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In a cylindrical region of radius $R=5.0\mathrm{cm}$ there is a uniform electric field, parallel to the axis, that grows at the rate $\frac{dE}{dt}=2.0\cdot 10^{12}V/(\mathrm{m}\cdot \mathrm{s})$; outside the region the electric field is zero and there are no currents. Compute the magnitude of the magnetic field at distance $r=8.0\mathrm{cm}$ from the axis.

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A radio station broadcasts at the frequency $f=98\mathrm{MHz}$. Compute the wavelength of the emitted waves in vacuum.

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A microwave oven operates at the frequency $f=2.45\mathrm{GHz}$. Compute the wavelength in vacuum and state the band of the electromagnetic spectrum to which it belongs.

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The electric field of a harmonic plane wave in vacuum has amplitude $E_0=450V/m$. Compute the amplitude of the magnetic field.

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A harmonic plane wave in vacuum has an electric field of amplitude $E_0=60V/m$. Compute the intensity of the wave.

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A transmitter, which can be treated as an isotropic source, emits the average power $P=50\mathrm{kW}$. Neglecting absorption, compute the intensity and the amplitude of the electric field at distance $r=10\mathrm{km}$.

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A laser beam of power $P=2.0\mathrm{W}$ is incident perpendicularly on a target that absorbs it completely. Compute the force exerted by the beam on the target.

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Outside the Earth’s atmosphere solar radiation has intensity $I=1.36kW/{\mathrm{m}}^2$. Compute the average electromagnetic energy density.

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A radar pulse is sent toward the Moon, which is at distance $d=3.84\cdot 10^8\mathrm{m}$, and is reflected by it. Compute after how much time the echo returns to the starting point.

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In vacuum the electric field of a plane wave is

$$\vec{E}(x,t)=30\sin \left(1.0\cdot 10^{7}x-\omega t\right)\hat{ȷ}V/m,$$

with $x$ in meters and $t$ in seconds. Compute the wavelength and the angular frequency, and write the magnetic field.

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