Physics · Electromagnetic Waves · NEET
You get B_rms, not B_peak. The relation E = cB connects fields of the SAME type: E_rms/c = B_rms, and E0/c = B0. So dividing an RMS electric field by c gives an RMS magnetic field. To reach the peak B0 you must still multiply by √2. Mixing them (E_rms/c = B0) is the most common mistake.
Because the field varies as a sine wave, E = E0 sin(kx − ωt). The average of sin² over a full cycle is 1/2, so the root-mean-square is √(E0²/2) = E0/√2. The same √2 factor applies to B, to AC voltage, and to AC current. So E_rms = E0/1.41 and E0 = 1.41·E_rms.
It works for peak, RMS, and even instantaneous values, because at every instant the electric field is exactly c times the magnetic field. So E0 = cB0, E_rms = cB_rms, and E(t) = cB(t). You can pick whichever version matches the values given in the question.
Combine both relations: B_peak = B0 = E0/c = (√2·E_rms)/c. So multiply the RMS electric field by √2, then divide by c. Order does not matter, but never skip the √2 — that single factor is the whole trap.
No. The simple time-average of a sine field over a full cycle is zero (it swings equally positive and negative). RMS is the root of the mean of the square, which is not zero — it is E0/√2. RMS is the value used for energy and intensity because energy depends on E², never on E alone.
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 (c = 3×10⁸ m/s)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
E_rms = E0/√2, or equivalently E0 = √2·E_rms ≈ 1.41·E_rms. The identical form holds for the magnetic field: B_rms = B0/√2.
E = cB at every instant, so also E0 = cB0 and E_rms = cB_rms, where c = 3×10⁸ m/s is the speed of light. This makes E far larger in number than B.
Use B0 = (√2·E_rms)/c. First multiply E_rms by √2 to reach E0, then divide by c to reach B0.
Energy density and intensity depend on the square of the field. The RMS value is the effective field for energy, so I and average energy density are written using E_rms, not the peak.
Indirectly. Intensity uses E_rms² = E0²/2, so the ½ (which is (1/√2)²) already carries the same idea. Always decide first whether the given field is peak or RMS before squaring.
