Exam 31: Electromagnetic Waves

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 x 10⁸ m/s)

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 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 x 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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)

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?

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

In an electromagnetic wave, the electric and magnetic fields are oriented such that they are

An electromagnetic wave has a peak electric field of 3.0 kV/m. What is the intensity of the wave? (c = 3.0 x 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 power output 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 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)

The y-component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation Ey = (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?

The magnitude of the electric field at a point P for a certain electromagnetic wave is 570 N/C. What is the magnitude of the magnetic field for that wave at P? (c = 3.0 x 10⁸ m/s)

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)

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 x 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)

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 0.63 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 magnetic field amplitude of the signal at that point? (c = 3.0 x 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A very small source of light that radiates uniformly in all directions produces an electric field amplitude of 2.96 V/m at a point 33.0 m from the source. What is the power output from the source? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

If the electric field and magnetic field of an electromagnetic wave are given by E = E₀ sin(kx - ωt) and B = B₀ sin(kx - ωt), and if the value of E0 is 51 µV/m, what is the value of B₀? (c = 3.0 x 10⁸ m/s)

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 amplitude of the electric field? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Given that the wavelengths of visible light range from 400 nm to 700 nm, what is the highest frequency of visible light? (c = 3.0 x 10⁸ m/s)