Exam 34: Electromagnetic Fields and Waves

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.939 W/m². The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. How much total electromagnetic energy falls on the area during 1.0 minute? (c = 3.0 x 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

If a beam of electromagnetic radiation has an intensity of 120 W/m², what is the maximum value of the electric field? (c = 3.0 x 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 following are positioned in sequence: A source of a beam of natural light of intensity I₀; three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, from the perspective of the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. Polarizer B is set so that the beam intensity is zero at the observer. Which of the following pairs of angles are possible axis angle settings of polarizer B?

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 µJ. What magnitude force does the microwave beam exert on the base of the oven? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 µJ. What is the intensity of the microwave beam? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A 7.5 × 10¹⁴ Hz laser emits a 7.7-μs pulse, 5.0 mm in diameter, with a beam energy density of 0.51 J/m³. What is the amplitude of the electric field of the emitted waves? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

If an electromagnetic wave has components E_y = E₀ sin(kx - ωt) and B_z = B₀ sin(kx - ωt), in what direction is it traveling?

An electromagnetic wave is propagating towards the west. At a certain moment the direction of the magnetic field vector associated with this wave points vertically up. The direction of the electric field vector of this wave is

The total electromagnetic power emitted by the sun is 3.8 × 10²⁶ W. What is the radiation pressure on a totally absorbing satellite at the orbit of Mercury, which has an orbital radius of 5.8 × 10¹⁰ m? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

The average intensity of the sunlight in Miami, Florida, is 1.04 kW/m². For surfaces on which the light is all absorbed, what is the average value of the radiation pressure due to this sunlight in Miami? (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 x 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?