Electromagnetic Waves Problem Solutions

Summary

This video explores key concepts of electromagnetic waves, detailing calculations for electric and magnetic field amplitudes. It explains the relationship between the two fields, showcasing practical applications such as microwave ovens and radio receivers. Viewers learn how to derive the electric field amplitude from a given magnetic field amplitude and vice versa. Additionally, the video covers intensity calculations for microwave radiation and how to determine distances from point sources based on electric field strength. The engaging and informative approach makes complex physics accessible, enhancing understanding of electromagnetic wave behavior.

Takeaways

• ⚡ The electric field amplitude of an electromagnetic wave can be calculated using the formula: E = c * B, where E is the electric field amplitude, c is the speed of light, and B is the magnetic field amplitude.
• 📏 An electromagnetic wave with a magnetic field amplitude of 2 mT results in an electric field strength of 6.0 x 10^5 V/m.
• 🧲 To find the magnetic field amplitude from the electric field amplitude, use the formula: B = E / c.
• 🔍 A microwave oven operating at 2.4 GHz with an intensity of 2500 W/m² results in an oscillating electric field amplitude of approximately 1.37 x 10^3 V/m.
• 📉 The oscillating magnetic field amplitude can be derived from the electric field amplitude, yielding a value of 4.6 x 10^-6 T.
• 🚨 The maximum allowed leakage of microwave radiation from an oven is 5 mW/cm², which equals 5 x 10^7 W/m² after conversion.
• 📊 The amplitude of the oscillating electric field from the maximum leakage is approximately 0.0019 V/m, indicating a small intensity.
• 🌌 The distance from a point source of electromagnetic waves where the electric field amplitude is 0.01 V/m can be calculated, resulting in a distance of 77 m.
• 🔒 The intensity of the smallest detectable signal by a radio receiver with an electric field amplitude of 300 µV/m is 1.2 x 10^-10 W/m².
• 📡 The information covers fundamental relationships between electric and magnetic fields in electromagnetic waves and their practical applications in technology.

Q & A

What is the relationship between the electric field amplitude and the magnetic field amplitude in electromagnetic waves?

The electric field amplitude (E) is related to the magnetic field amplitude (B) by the equation E = cB, where c is the speed of light.

How do you calculate the electric field amplitude from the magnetic field amplitude?

To calculate the electric field amplitude from the magnetic field amplitude, you multiply the magnetic field amplitude (B) by the speed of light (c): E = cB.

What is the formula to calculate the magnetic field amplitude given an electric field amplitude?

The formula to calculate the magnetic field amplitude (B) given the electric field amplitude (E) is B = E/c, where c is the speed of light.

How can you derive the electric field amplitude from the intensity of a microwave oven?

The electric field amplitude can be derived from the intensity (I) using the formula E = sqrt((2I) / (ε₀c)), where ε₀ is the permittivity of free space and c is the speed of light.

What unit conversions are necessary when calculating intensity from milliwatts per square centimeter to watts per square meter?

To convert from milliwatts per square centimeter to watts per square meter, you multiply by 10 (to convert milliwatts to watts) and by 10,000 (to convert square centimeters to square meters), resulting in a factor of 10^7.

What is the maximum allowed leakage of microwave radiation from a microwave oven, and how is it calculated?

The maximum allowed leakage of microwave radiation is about 5 mW/cm², which can be converted to watts per square meter for calculations.

How do you find the distance from a point source of electromagnetic waves given the electric field amplitude?

The distance (r) can be found using the formula r = sqrt((2P) / (4πI)), where P is the power of the source and I is the intensity calculated using the electric field amplitude.

What is the intensity of the smallest detectable signal for a radio receiver that can detect electric field amplitudes of 300 µV/m?

The intensity of the smallest detectable signal can be calculated using the formula I = (cε₀E²) / 2, resulting in an intensity of approximately 1.2 × 10^{-10} W/m².

What constants are used in the calculations involving electric and magnetic fields?

The constants used in the calculations include the speed of light (c = 3 × 10^8 m/s) and the permittivity of free space (ε₀ = 8.85 × 10^{-12} F/m).

Why is it important to understand the relationships between electric field amplitude, magnetic field amplitude, and intensity?

Understanding these relationships is crucial for applications in communications, safety, and technology, as they govern how electromagnetic waves interact with the environment and are detected by devices.