Concept #1: Energy Carried by Electromagnetic Waves

Practice: A 100 W lightbulb actually emits around only 10 W of light. What is the intensity of the light 1 cm away if the light is emitted perfectly spherically? What is the magnitude of the electric field emitted by the lightbulb? What about the magnetic field?

You are trying to estimate the efficiency of a lightbulb by measuring the power of the light emitted vs the power consumed by the bulb. You have a circular detector with a radius of 12 cm and you measure an intensity of 1.7 kW/m2 from a distance of 1.5 m. If the lightbulb pulls 150 W of power from an outlet, what is the efficiency of the lightbulb?

Two sources of sinusoidal electromagnetic waves have average powers of P1 = 100.0 W and P2 = 320 W and emit uniformly in all directions. At the same distance from the source what is the ratio of maximum electric fields E2 to that of E1 i.e... E2/E1

Two sources of sinusoidal electromagnetic waves have average powers of P1 = 100.0 W and P2 = 320 W and emit uniformly in all directions. For the electromagnetic wave with P 1 = 100.0 W find the ratio of intensity S1 10 m away from the source to the intensity S 1 100m away from the source, i.e. S1 (10m)/S1(100m) (Hint: Area of sphere 4πR2)

An 800-kHz signal is detected at a point 7.7 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 550 mV/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. The intensity of the radio signal at that point is closest to:
A) 2.0 x 10-4 W/m2
B) 5.7 x 10-4 W/m2
C) 8.0 x 10-4 W/m2
D) 2.8 x 10-4 W/m2
E) 4.0 x 10-4 W/m2

An isotropic source of electromagnetic radiation emits light that, when measured at 10 cm from the source, carries an electric field amplitude of 1.0x103 N/C and a magnetic field amplitude of 3.33x10-6 T.
(a) What is the average Poynting flux, Sav, through a sphere of radius 10 cm?
(b) How much light-energy is emitted by the source per second?
(c) If the source is 80% efficient at converting electrical power into light-energy, how much power must be supplied to the source?

An open MRI scanner can produce a magnetic field strength of up to 3 T. If the space between the poles of the magnet (where the patient lies) is cylindrical, with a diameter of 2 m and a height of 70 cm, answer the following questions:
(a) What is the magnetic energy density within this MRI?
(b) What is the total magnetic energy contained within the MRI?

Calculate the total average power of the station's radio transmitter.
a. <P> = 330 MW
b. <P> = 485 MW
c. <P> = 667 MW
d. <P> = 802 MW
e. <P> = 950 MW

A large electromagnet has a 22 T magnetic field between its poles. What is the magnetic energy density between the poles?
A) 240 J/cm3
B) 30,000 J/cm3
C) 88 J/cm3
D) 190 J/cm3

The energy flow per unit time per unit area (S) of an electromagnetic wave has an average value of 695 mW/m2. The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. The total energy that traverses the area in a time interval of one minute is closest to:
A) 130 J
B) 250 J
C) 160 J
D) 220 J
E) 190 J

A point source emits electromagnetic radiation uniformly in all directions. If the power output of the source is 960 W, what are the amplitudes of the electric and magnetic fields in the wave at a distance of 15.0 m from the source? (The surface area of a sphere that has radius R is 4πR2, ε0 = 8.854 x 1012 C2/(N•m2). μ0 = 4π x 10-7 T•m/A.)
electric field amplitude = _______________
magnetic field amplitude = _______________

A laser beam has a wavelength of 633 nm and a power of 0.500 mW spread uniformly over a circle 1.20 mm in diameter. This beam falls perpendicularly on a perfectly reflecting piece of paper having twice the diameter of the laser beam and a mass of 1.50 mg. What are the amplitudes of the electric and magnetic fields in this laser beam?

A large electromagnet has a 22T magnetic field between its poles. What is the magnetic energy density between the poles?A) 88 J/cm3B) 190 J/cm3C) 30,000 J/cm3D) 240 J/cm3

An 800-kHz radio signal is detected at a point 4.5 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 200 mV/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. The intensity of the radio signal at that point is closest to:A) 3.8 x 10-5 W/m2B) 5.3 x 10-5 W/m2C) 7.5 x 10-5 W/m2D) 1.1 x 10-4 W/m2E) 2.8 x 10-5 W/m2

A point source of electromagnetic waves emits waves uniformly in all directions. At a distance of 10.0 m from the source the magnetic field amplitude for the waves is 4.0 x 10-8 T. (Note: c = 3.00 x 108 m/s, ε0 = 8.854 x 10-12 C2 / (N•m2), μ0 = 4π x 10-7 T•m/A)What is the electric field amplitude at this point, 10.0 m from the source?

A point source of electromagnetic waves emits waves uniformly in all directions. At a distance of 10.0 m from the source the magnetic field amplitude for the waves is 4.0 x 10-8 T. (Note: c = 3.00 x 108 m/s, ε0 = 8.854 x 10-12 C2 / (N•m2), μ0 = 4π x 10-7 T•m/A)What is the intensity of the wave at this point, 10.0 m from the source?

Sinusoidal electromagnetic waves from a radio station pass perpendicularly through an open window that has area 0.200 m2. At the window, the magnetic field of the wave has amplitude Bmax = 7.00 x 10-10 T. How much energy does the wave carry through the window in 2.00 minutes? (Note: ε0 = 8.854 x 10-12 C2 / N•m2 and μ0 = 4π x 10-7 T•m/A)

The energy density of an electromagnetic wave isA) equally divided between the magnetic and the electric fields.B) entirely in the magnetic field.C) 1/4 in the electric field and 3/4 in the magnetic field.D) entirely in the electric field.E) 1/4 in the magnetic field and 3/4 in the electric field.

If the magnetic field in a traveling electromagnetic wave has a maximum value of 16.5 nT. What is the maximum value of the electric field associated with this wave? (c = 3.00 x 108 m/s)A) 5.5 x 10-17 V/mB) 4.95 V/mC) 0.495 V/mD) 55.0 x 10-16 VmE) 55.0 x 10-15 Vm

Sinusoidal electromagnetic waves from a radio station process pass perpendicularly through an open window that has area 0.400 m2. The intensity of the wave is constant over the area of the window. The wave carries 0.800 J of energy through the window in 5.00 s. (Note: ε0 = 8.854 x 10-12 C2/N•m2 and μ0 = 4π x 10-7 T•m/A) What is the intensity of the wave at the window?

Sinusoidal electromagnetic waves from a radio station process pass perpendicularly through an open window that has area 0.400 m2. The intensity of the wave is constant over the area of the window. The wave carries 0.800 J of energy through the window in 5.00 s. (Note: ε0 = 8.854 x 10-12 C2/N•m2 and μ0 = 4π x 10-7 T•m/A) At the window, what is the amplitude of the magnetic field of the wave?

Sinusoidal electromagnetic waves from a radio station process pass perpendicularly through an open window that has area 0.400 m2. The intensity of the wave is constant over the area of the window. The wave carries 0.800 J of energy through the window in 5.00 s. (Note: ε0 = 8.854 x 10-12 C2/N•m2 and μ0 = 4π x 10-7 T•m/A) The window is replaced b y a mirror that has area 0.400 m2. What is the force that the wave exerts on the mirror, if the wave is totally reflected?

A cylindrical laser beam has diameter 8.00 mm. The average energy density in the beam is 8.00 x 10-3 J/m3. What is the amplitude of the magnetic field in the beam?

A sinusoidal electromagnetic wave has intensity I = 100 W/m 2 and an electric field amplitude E. What is the electric field amplitude of a 50 W/m 2 electromagnetic wave with the same wavelength?(a) 4E(b) 2E(c) 2√2E(d) √2E(e) E / (2√2) (f) E / √2(g) E / 4(h) E / 2

A cylindrical laser beam has diameter 8.00 mm. The average energy density in the beam is 8.00 x 10-3 J/m3. What is the power output of the laser?

The power radiated by a star is 8.0 x 1030 W. What is the intensity of the radiation from this star at a distance of 1.0 x 1012 m from the star?(a) 8.0 x 1018 W/m2(b) 8.0 x 106 W/m2(c) 2.5 x 106 W/m2(d) 6.4 x 105 W/m2(e) 3.2 x 105 W/m2(f) none of the above answers

The graph shows the intensity of transmitted light of different colors (wavelengths) as a function of depth x in meters for absorption in water. Approximately what is the absorption coefficient α for UV (ultraviolet) LIGHT, given the exponential transmission I(x) = I0e−αx ?
A. 2 m-1
B. 10-6 m-1
C. 0.003 m-1
D. 50 m-1
E. 0.025 m-1

A laser beam has a wavelength of 633 nm and a power of 0.500 mW spread uniformly over a circle 1.20 mm in diameter. This beam falls perpendicularly on a perfectly reflecting piece of paper having twice the diameter of the laser beam and a mass of 1.50 mg. What acceleration does the laser beam give to the paper?