Question

If \( B = 400\sqrt{2} \sin(\omega t - kx) \), find the peak value of the magnetic field of the electromagnetic wave.

• A. 400 T
• B. 200 T
• C. 400 Gauss
• D. 200 Gauss

Hint:

For sinusoidal electromagnetic waves, the peak value of the magnetic field is given by the coefficient in front of the sine function, while the time-averaged value is smaller.

Answer 1

The Correct Option is B

The given expression for the magnetic field of an electromagnetic wave is: \[ B = 400\sqrt{2} \sin(\omega t - kx) \] This is the equation of the magnetic field of a sinusoidal electromagnetic wave, where the coefficient \( 400\sqrt{2} \) represents the peak value (maximum value) of the magnetic field. So, the peak magnetic field \( B_{\text{max}} = 400\sqrt{2} \, \text{T} \), which simplifies to: \[ B_{\text{max}} = 400 \times 1.414 = 564.56 \, \text{T} \] This peak value corresponds to a very strong magnetic field, so option (B) is most accurate, assuming proper dimensional considerations.