The amplitude of the magnetic field part of a harmonic electromagnetic wave in vaccum is B 0 = 480 nT. Find the amplitude of the electric field part of the wave?
Electromagnetic Wave Fields in Vacuum
An electromagnetic (EM) wave consists of oscillating electric and magnetic fields that are perpendicular to each other and also perpendicular to the direction of wave propagation. In a vacuum, these waves travel at a constant speed, which is the speed of light.
Magnetic Field Amplitude Given
The problem provides the amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum. This value is given as:
- Amplitude of magnetic field, \(B_0 = 480 \text{ nT}\)
To perform calculations, it is essential to convert the magnetic field amplitude from nanoTesla (nT) to Tesla (T). We know that \(1 \text{ nT} = 10^{-9} \text{ T}\).
Therefore, \(B_0 = 480 \times 10^{-9} \text{ T}\).
Electric Field Amplitude Calculation
In a vacuum, the amplitudes of the electric field (\(E_0\)) and the magnetic field (\(B_0\)) of an electromagnetic wave are directly related by the speed of light (\(c\)). The fundamental relationship is given by the formula:
\[E_0 = c \times B_0\]
Where:
- \(E_0\) is the amplitude of the electric field in Newtons per Coulomb (N/C) or Volts per meter (V/m).
- \(c\) is the speed of light in vacuum, which is approximately \(3 \times 10^8 \text{ m/s}\).
- \(B_0\) is the amplitude of the magnetic field in Tesla (T).
Now, let's substitute the given value of \(B_0\) and the speed of light \(c\) into the formula to find the amplitude of the electric field:
\[E_0 = (3 \times 10^8 \text{ m/s}) \times (480 \times 10^{-9} \text{ T})\]
Performing the multiplication:
\[E_0 = (3 \times 480) \times (10^8 \times 10^{-9}) \text{ N/C}\]
\[E_0 = 1440 \times 10^{(8 - 9)} \text{ N/C}\]
\[E_0 = 1440 \times 10^{-1} \text{ N/C}\]
\[E_0 = 144 \text{ N/C}\]
Summary of Calculation
| Parameter | Value | Unit |
|---|---|---|
| Magnetic Field Amplitude (\(B_0\)) | \(480\) | nT |
| Magnetic Field Amplitude (\(B_0\)) (converted) | \(480 \times 10^{-9}\) | T |
| Speed of Light (\(c\)) | \(3 \times 10^8\) | m/s |
| Electric Field Amplitude (\(E_0\)) | \(144\) | N/C |
The calculated amplitude of the electric field part of the wave is \(144 \text{ N/C}\).
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