Wavelength, frequency, and E field amplitude from magnetic field equation

In summary, we discussed the magnetic field of an electromagnetic wave in a vacuum and its equation, B_z= ( 3.0 uT )*sin(( 1.00*107)x - omega*t). We also determined that the wavelength is related to the wave number, k, and the frequency is related to the angular frequency, omega. Additionally, we found that the amplitude of the E field is equal to the speed of light, c, multiplied by the amplitude of B. The frequency and wavelength are related through the equation f = c/lambda. Finally, we determined that to find the amplitude of E, we need to know the amplitude of B.
  • #1
Linus Pauling
190
0
1. The magnetic field of an electromagnetic wave in a vacuum is B_z= ( 3.0 uT )*sin(( 1.00*107)x - omega*t) , where x is in m and t is in s.

What is the wavelength and frequency of this magnetic wave? What is the amplitude of the E field?



2. wavelength = 2pi/k
frequency = f = 1/T = omega/2pi
E = cB



3. k = 1*107, so lambda = 2pi/k = 6.28*10-7

How do I find frequency without knowing omega?

How do I go about obtaining an actual value for E0? It doesn't seem like E =cB will be enough here...
 
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  • #2
How are the frequency and the wavelength related?

ehild
 
  • #3
Yeah I got frequency since I posted this from c = lamba*f but I'm stuck on E still
 
  • #4
You need the amplitude of the E field and it is c times the amplitude of B. What is the amplitude of B?

ehild
 

What is the relationship between wavelength, frequency, and E field amplitude from the magnetic field equation?

The relationship between wavelength, frequency, and E field amplitude from the magnetic field equation is known as the electromagnetic wave equation. This equation states that the wavelength (λ) is equal to the speed of light (c) divided by the frequency (f), or λ = c/f. The E field amplitude (E0) can be calculated by multiplying the magnetic field amplitude (B0) by the speed of light (c), or E0 = B0 x c.

How do changes in wavelength or frequency affect the E field amplitude?

Changes in wavelength or frequency can directly impact the E field amplitude. According to the electromagnetic wave equation, as the frequency increases, the wavelength decreases and vice versa. This means that the E field amplitude will also change accordingly, increasing as the frequency increases and decreasing as the wavelength increases.

Can the E field amplitude and magnetic field amplitude be different for the same electromagnetic wave?

Yes, the E field amplitude and magnetic field amplitude can be different for the same electromagnetic wave. This is because the E field and magnetic field are perpendicular to each other and have different units of measurement. The E field is measured in volts per meter (V/m), while the magnetic field is measured in tesla (T).

How is the E field amplitude related to the intensity of an electromagnetic wave?

The E field amplitude is directly proportional to the intensity of an electromagnetic wave. This means that as the E field amplitude increases, the intensity of the wave also increases. The intensity is a measure of the energy carried by the wave and is proportional to the square of the E field amplitude.

What factors can affect the E field amplitude and magnetic field amplitude of an electromagnetic wave?

The E field amplitude and magnetic field amplitude of an electromagnetic wave can be affected by several factors. These include the distance from the source of the wave, the medium through which the wave is traveling, and any obstructions or interference in the path of the wave. Additionally, the frequency and wavelength of the wave can also impact the E field and magnetic field amplitudes.

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