a plane electromagnetic wave is traveling in a vacuum. the magnetic field is directed along the z-axis and given by: B_z = 3.0 mu T sin(1.0 times 10^7 x - 3.0 times 10^15 t) True / False The wavelength lambda of the wave is 1.0 times 10^7 meters True / False The frequency f of the wave is 3.0 times 10^15 Hz. True / False The direction of the electric field is along the x-axis. True / False Doubling the magnetic field strength

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09-12-2022
Physics

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a plane electromagnetic wave is traveling in a vacuum. the magnetic field is directed along the z-axis and given by: B_z = 3.0 mu T sin(1.0 times 10^7 x - 3.0 times 10^15 t) True / False The wavelength lambda of the wave is 1.0 times 10^7 meters True / False The frequency f of the wave is 3.0 times 10^15 Hz. True / False The direction of the electric field is along the x-axis. True / False Doubling the magnetic field strength

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-19T02:06:28+01:00

In a vacuum, an electromagnetic wave is moving through the air. The wavelength is 1x10^7m and the frequency is 3x10^15Hz while the direction of the electric field is along the z-axis.

Given the magnetic field along z axis (B) = 3.0muTsin(1.0x10^7x - 3.0*10^15 t)

The formula for magnetic field is B = B0sin(wt+kx)

For direction of wave by comparing the equations we have

kx +(- 3.0 x 10^15 ) = 0

x = 3.0 x 10^15 /k in positive direction of x axis

The direction of propogation is along x axis and the magnetic field in y axis. The electric field is in both directions. So E along z axis

B0 = 3x10-7x4πT

ω = -3.0 x 10^15

∧ = 2π/k = 2x3.14/1.0x10^7 = 0.68/1.0x10^7 = 0.68x10-7

The wavelength ∧ of the wave is = 0.68x10-7m

frequency (f) = c/∧ = 3x10^8/0.68x10-7 = 4.41x10^15Hz

The frequency f of the wave is 4.41x10^15Hz

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