24.4 Energy in Electromagnetic Waves

An old microwave oven outputs only half the electric field it used to. How much longer does it take to cook things in this microwave oven?

1. Four times as long
2. Twice as long
3. Half the time
4. One fourth the time

What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?

Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0.250 mW. (a) If such a laser beam is projected onto a circular spot 1.00 mm in diameter, what is its intensity? (b) Find the peak magnetic field strength. (c) Find the peak electric field strength.

Suppose the maximum safe intensity of microwaves for human exposure is taken to be $1 . \text{00 W} /\text{m}^{2}$. (a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection. (b…

Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of $1 . \text{00} \times \text{10}^{\text{11}} \text{ V} / \text{m}$ for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c)…

Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects. (a) Show that the intensity is inversely proportional to $r^{2}$, the distance from the source squared. (b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to $r$.

What capacitance is needed in series with an $\text{800} - \mu \text{H}$ inductor to form a circuit that radiates a wavelength of 196 m?

Assume the mostly infrared radiation from a heat lamp acts like a continuous wave with wavelength $1.50 \mu \text{m}$. (a) If the lamp’s 200-W output is focused on a person’s shoulder, over a circular area 25.0 cm in diameter, what is the intensity in $\text{W}/\text{m}^{2}$? (b) What is the peak electric field strength? (c) Find the peak magnetic field strength. (d) How long will it take to increase the temperature of the 4.00-kg sho…

Electromagnetic radiation from a 5.00-mW laser is concentrated on a $1 . \text{00} -\text{mm}^{2}$ area. (a) What is the intensity in $\text{W}/\text{m}^{2}$? (b) Suppose a 2.00-nC static charge is in the beam. What is the maximum electric force it experiences? (c) If the static charge moves at 400 m/s, what maximum magnetic force can it feel?

If electric and magnetic field strengths vary sinusoidally in time, being zero at $t = 0$, then $E = E_{0} \text{sin} 2π \text{ft}$ and $B = B_{0} \text{sin} 2π \text{ft}$. Let $f = 1 . \text{00 GHz}$ here. (a) When are the field strengths first zero? (b) When do they reach their most negative value? (c) How much time is needed for them to complete one cycle?

The peak magnetic field strength in a residential microwave oven is $9 . \text{20} \times \text{10}^{- 5} \text{ T}$. (a) What is the intensity of the microwave? (b) What is unreasonable about this result? (c) What is wrong about the premise?

An $\text{LC}$ circuit containing a 1.00-pF capacitor oscillates at such a frequency that it radiates at a 300-nm wavelength. (a) What is the inductance of the circuit? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) Find the magnetic field strength when the electric field strength is 1,250 V/m. (b) If E is increased, would B be increased, decreased, or remain the same? (c) By what factor would the change in part b be, if any?