Answer:
Step-by-step explanation:
To calculate the electric field amplitude (E), we can use the relationship between the electric field amplitude and the magnetic field amplitude in an electromagnetic wave:
E = c * B
Where:
E is the electric field amplitude,
B is the magnetic field amplitude,
c is the speed of light in vacuum (approximately 3.0 x 10^8 m/s).
Given:
B = 100 nT = 100 x 10^-9 T
Substituting the values into the equation:
E = (3.0 x 10^8 m/s) * (100 x 10^-9 T)
E = 30 V/m
The electric field amplitude is 30 V/m.
Next, to calculate the energy density of the electric field (uE), we use the formula:
uE = (1/2) * ε0 * E^2
Where:
uE is the energy density of the electric field,
ε0 is the vacuum permittivity (approximately 8.854 x 10^-12 C^2/(N*m^2)),
E is the electric field amplitude.
Substituting the values:
uE = (1/2) * (8.854 x 10^-12 C^2/(N*m^2)) * (30 V/m)^2
uE ≈ 3.99 x 10^-10 J/m^3
The energy density of the electric field is approximately 3.99 x 10^-10 J/m^3.
To calculate the energy density of the magnetic field (uB), we use the formula:
uB = (1/2) * (1/μ0) * B^2
Where:
uB is the energy density of the magnetic field,
μ0 is the vacuum permeability (approximately 4π x 10^-7 T*m/A),
B is the magnetic field amplitude.
Substituting the values:
uB = (1/2) * (1/(4π x 10^-7 T*m/A)) * (100 x 10^-9 T)^2
uB ≈ 1.59 x 10^-13 J/m^3
The energy density of the magnetic field is approximately 1.59 x 10^-13 J/m^3.
Finally, the total energy density (u) of the wave is the sum of the energy densities of the electric and magnetic fields:
u = uE + uB
u ≈ 3.99 x 10^-10 J/m^3 + 1.59 x 10^-13 J/m^3
u ≈ 3.99 x 10^-10 J/m^3
The total energy density of the wave is approximately 3.99 x 10^-10 J/m^3.