Physics · Electromagnetic Waves · NEET
It is a ratio, not a product: E0/B0 = c. The electric amplitude divided by the magnetic amplitude equals the speed of light. So E0 = c B0 and B0 = E0/c. A product E0 x B0 has units of (V/m)(T) which is not m/s, so it can never equal c. Quick check: c is a big number (3 x 10^8), so E0 must be much bigger than B0 - the ratio E0/B0 gives that big number correctly.
Because B0 = E0/c and you are dividing by a huge number c = 3 x 10^8. For example, E0 = 3 V/m gives B0 = 3 / (3 x 10^8) = 10^-8 T. The magnetic field is not weak physically - it carries exactly the same energy as the electric field. Its numerical value just looks small because of the units and the division by c.
Both. E and B in an EM wave oscillate in phase - they reach zero together and peak together. So at every instant E = cB, and in particular for the peaks E0 = cB0. This is why you can use either the instantaneous values or the amplitudes; the ratio E/B = c stays constant throughout the wave.
No. Inside a medium the wave slows to speed v = c/n, and there the ratio becomes E/B = v (not c). So E0/B0 = v = c/n in a medium. In vacuum or free space, v = c, so E0/B0 = c. NEET numericals usually say 'free space' or 'vacuum', so use c there; only switch to v if the question gives a medium.
The ratio E/B = c holds for rms values too, so B_rms = E_rms/c. Then convert to peak using B0 = sqrt(2) x B_rms (since peak = sqrt(2) x rms for a sine wave). This exact chain appeared in NEET 2017: E_rms = 6 V/m gave B_rms = 2 x 10^-8 T, then B0 = sqrt(2) x 2 x 10^-8 = 2.83 x 10^-8 T.
In an electromagnetic wave in free space the root mean square value of the electric field is E_rms = 6 V/m. The peak value of the magnetic field is
In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of 2.0 x 10^10 Hz and amplitude 48 V/m. Then the amplitude of the oscillating magnetic field is (speed of light = 3 x 10^8 m/s)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
E0/B0 = c and E = cB at every instant, where c = 3 x 10^8 m/s is the speed of light in free space. The electric amplitude equals c times the magnetic amplitude.
It comes from Maxwell's equations for a plane wave: the changing E field creates B and the changing B field creates E, and consistency forces their amplitude ratio to equal the wave speed c. The same c also equals 1/sqrt(mu0 epsilon0).
Divide E0 by c: B0 = E0 / (3 x 10^8). For example, E0 = 48 V/m gives B0 = 1.6 x 10^-7 T. To go the other way, E0 = c x B0.
Yes, in SI units. Because E0 = c B0 and c is about 3 x 10^8, the number for E is about 10^8 times the number for B. So E is a few V/m while B is around 10^-8 T. Despite this, both fields carry equal energy.
No. E0/B0 = c is independent of frequency. Whether the wave is a radio wave or a gamma ray, in free space the amplitude ratio is always c. Frequency values in a question are often distractors.
