A plane electromagnetic wave travels through vacuum

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

A plane electromagnetic wave travels through vacuum. The peak value of its magnetic field is measured to be

B_0 = 2.0 \times 10^{-7}\,\text{T}

and the time taken for one complete oscillation of the fields is

T = 2.5\,\text{ns}

. Answer the following: (i) Calculate the angular frequency

\omega

of the wave. (ii) Determine the numerical values of the frequency

\nu

and the wavelength

\lambda

. (iii) Find the magnitude of the peak electric field

E_0

associated with the wave. (iv) Using your value of

\lambda

, compute the wave number

k

and verify that it is consistent with the values of

\omega

and

\nu

obtained earlier. (v) If the measured value of

B_0

carries an uncertainty of

\pm2\%

, estimate the resulting percentage uncertainty in the value of

E_0

. Assume all other quantities are exact.