Question

The magnetic field in a plane electromagnetic wave is \[ B_y = (3.5 \times 10^{-7}) \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{T}. \] The corresponding electric field will be:

• A. \( E_y = 1.17 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m} \)
• B. \( E_z = 105 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m} \)
• C. \( E_z = 1.17 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m} \)
• D. \( E_y = 10.5 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m} \)

Answer 1

The Correct Option is B

Solution: For an electromagnetic wave, the magnetic and electric fields are related by the equation:

\( E = cB \),

where \( c \) is the speed of light in a vacuum.

Given:

\( B_y = (3.5 \times 10^{-7}) \sin (1.5 \times 10^3 x + 0.5 \times 10^{11} t) \, \text{T} \),

we know that the amplitude of the electric field is:

\( E_z = c B_y = (3 \times 10^8)(3.5 \times 10^{-7}) \, \text{V/m} = 105 \, \text{V/m}. \)

Thus, the correct electric field is:

\( E_z = 105 \sin (1.5 \times 10^3 x + 0.5 \times 10^{11} t) \, \text{V/m}. \)