Exam 31: Electromagnetic Fields and Waves

A laser with a power of 1.0 mW has a beam radius of 1.0 mm. What is the peak value of the electric field in that beam? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

An 800-kHz radio signal is detected at a point 8.5 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.90 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the average electromagnetic energy density at that point? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

When an electromagnetic wave falls on a white, perfectly reflecting surface, it exerts a force F on that surface. If the surface is now painted a perfectly absorbing black, what will be the force that the same wave will exert on the surface?

If the z-component of the magnetic field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation B_z(x, t) = (1.25 μT) cos[(3800 m^-1)x - (1.14 × 10-¹² rad/s)t], what is the largest that the y component of the electric field can be? (c = 3.0 × 10⁸ m/s)

An electromagnetic wave propagates along the +y direction as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field?

An 800-kHz radio signal is detected at a point 2.7 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.36 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the intensity of the radio signal at that point? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

The y-component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation E_y = (375 N/C) cos[kx - (2.20 × 10¹⁴ rad/s)t]. (c = 3.0 × 10⁸ m/s) (a) What is the largest that the x-component of the wave can be? (b) What is the largest that the z-component of the wave can be?

A radiometer has two square vanes (1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m² is incident normally upon the vanes. What is the radiation pressure on the blackened vane? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

An electromagnetic wave has a peak electric field of 3.0 kV/m. What is the intensity of the wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A capacitor is hooked up to a resistor and an AC voltage source as shown in the figure. The output of the source is given by V(t) = V₀ sin ωt. The plates of the capacitor are disks of radius R. Point P is directly between the two plates, equidistant from them and a distance R/2 from the center axis. At point P

A totally absorbing surface having an area of 7.7 cm² faces a small source of sinusoidal electromagnetic radiation that is 2.4 m away. At the surface, the electric field amplitude of the radiation is 84 V/m. (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) (a) What is the radiation pressure exerted on the surface? (b) What is the total power output of the source, if it is assumed to radiate uniformly in all directions?

A radiometer has two square vanes (1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m² is incident normally upon the vanes. What is the torque due to radiation pressure on the vane assembly about the vertical axis? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

If the intensity of an electromagnetic wave is 80 MW/m², what is the amplitude of the magnetic field of this wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Unpolarized light passes through three polarizing filters. The first one is oriented with a horizontal transmission axis, the second filter has its transmission axis 25.7° from the horizontal, and the third one has a vertical transmission axis. What percent of the light gets through this combination of filters?

The y component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation E_y = (375 N/C) cos[kx - (2.20 × 10¹⁴ rad/s)t]. What is the wavelength of this electromagnetic wave? (c = 3.0 × 10⁸ m/s)

A radiometer has two square vanes (each measuring 1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m² is incident normally upon the vanes. What is the electromagnetic power absorbed by the blackened vane? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

An 800-kHz radio signal is detected at a point 9.1 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.440 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the average total power radiated by the transmitter? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

In the figure, the orientation of the transmission axis for each of three polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarized with an intensity of 1000 W/m². What is the intensity of the beam after it has passed through the three polarizing sheets when θ₁ = 30°, θ₂ = 30° and θ₃ =60°?

Unpolarized light is incident upon two polarization filters that do not have their transmission axes aligned. If of the light passes through this combination of filters, what is the angle between the transmission axes of the filters?

A sinusoidal electromagnetic wave in vacuum delivers energy at an average rate of 5.00 µW/m². What are the amplitudes of the electric and magnetic fields of this wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)