A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x × 10⁻⁸ T. The value of x is ___________.

Solution

Physics sir · 3 steps

In an EM wave, E and B always move together: divide E by c and you have B.

1. E and B link. In a plane EM wave in free space, the electric and magnetic fields at any point and instant are tied by E = cB. This holds for the instantaneous values, not only the peak values.

   B = E/c = (6 V m⁻¹)/(3 × 10⁸ m s⁻¹) = 2 × 10⁻⁸ T

2. Frequency not needed. The 30 MHz only sets how fast the fields oscillate. The ratio E/B equals c at every frequency, so the frequency does not enter the calculation.
3. So. B = 2 × 10⁻⁸ T, so x = 2.

The idea to keep. For any EM wave in vacuum, B = E/c at every point and instant, whatever the frequency. Extra data like frequency is often given just to distract you.

Answer from the NTA final answer key. Solution by PrepWiser.