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Intensity of EM Waves quiz #1

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  • How do you calculate the intensity of an electromagnetic wave given its peak electric field strength, for example, if the peak electric field is 125 V/m?
    The intensity I of an electromagnetic wave with peak electric field E_max is given by I = 0.5 × c × ε₀ × E_max², where c is the speed of light and ε₀ is the permittivity of free space. For E_max = 125 V/m, plug the value into the formula to find the intensity.
  • How do you determine the intensity of light at a distance r from an isotropic point source such as a light bulb?
    For an isotropic point source emitting power P, the intensity I at distance r is I = P / (4πr²), where 4πr² is the surface area of a sphere centered on the source at radius r.
  • What is the intensity of electromagnetic waves inside a microwave oven operating at 2.4 GHz if the intensity is given as 2800 W/m²?
    The intensity inside the microwave oven is 2800 W/m². The frequency (2.4 GHz) is not needed to state the intensity, as it is already provided.
  • What is the general definition of intensity for any type of wave, including electromagnetic waves?
    Intensity is defined as the energy transferred per unit time per unit area, or equivalently, power per area. The standard unit for intensity is watts per square meter (W/m²).
  • Which formula relates the intensity of an electromagnetic wave to the maximum value of its magnetic field?
    The formula is I = 0.5 × c / μ₀ × B_max², where c is the speed of light, μ₀ is the permeability of free space, and B_max is the peak magnetic field. This equation is analogous to the electric field version but uses magnetic quantities.
  • How do you determine whether to use the surface area of a sphere or another area when calculating intensity from a light source?
    If the source emits equally in all directions (isotropic), use the surface area of a sphere (4πr²). For directional sources like flashlights or lasers, you must calculate the specific area illuminated by the beam.
  • What is the relationship between the root mean square (RMS) value and the maximum value for electric or magnetic fields in electromagnetic waves?
    The RMS value is equal to the maximum value divided by the square root of 2. This applies to both electric and magnetic fields: RMS = Max / √2.
  • How can you calculate the maximum value of the magnetic field (B_max) if you know the maximum electric field (E_max) in an electromagnetic wave?
    Use the relationship E_max = c × B_max, where c is the speed of light. Rearranging gives B_max = E_max / c.
  • What is the unit of the electric field when calculating its maximum value from intensity in electromagnetic waves?
    The unit of the electric field is newtons per coulomb (N/C). This is the standard SI unit for electric field strength.
  • Why is it important to distinguish between maximum and RMS values when solving electromagnetic wave intensity problems?
    Problems may specifically ask for either the maximum or RMS value, and using the wrong one can lead to incorrect answers. Always check which value is required and use the appropriate formula.