Question

Equation of electric field of a plane electromagnetic wave is \( E_y = 60 \sin(500x - 1.5 \times 10^{11}t) \, \text{V/m} \). Write the equation for the magnetic field of the wave.

Hint:

The magnetic field in an electromagnetic wave is always perpendicular to the electric field and the direction of wave propagation.

Answer 1

Step 1: Relationship Between Electric and Magnetic Fields.
For an electromagnetic wave, the electric field \( E \) and magnetic field \( B \) are related by the following equation: \[ B = \frac{E}{c} \] where \( c \) is the speed of light. The magnetic field oscillates perpendicular to both the electric field and the direction of propagation.
Step 2: Equation for the Magnetic Field.
Given \( E_y = 60 \sin(500x - 1.5 \times 10^{11}t) \), we can write the magnetic field equation as: \[ B_z = \frac{60}{3 \times 10^8} \sin(500x - 1.5 \times 10^{11}t) \] Simplifying this gives: \[ B_z = 2 \times 10^{-7} \sin(500x - 1.5 \times 10^{11}t) \, \text{T} \]