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Physics Question on Electromagnetic waves

The magnetic field in a plane electromagnetic wave is By=(3.5×10−7)sin⁡(1.5×103x+0.5×1011t) T.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

Ey=1.17sin⁡(1.5×103x+0.5×1011t) V/mE_y = 1.17 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m}

B

Ez=105sin⁡(1.5×103x+0.5×1011t) V/mE_z = 105 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m}

C

Ez=1.17sin⁡(1.5×103x+0.5×1011t) V/mE_z = 1.17 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m}

D

Ey=10.5sin⁡(1.5×103x+0.5×1011t) V/mE_y = 10.5 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m}

Answer

Ez=105sin⁡(1.5×103x+0.5×1011t) V/mE_z = 105 \sin \left( 1.5 \times 10^3 x + 0.5 \times 10^{11} t \right) \, \text{V/m}

Explanation

Solution

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

E=cBE = cB,

where cc is the speed of light in a vacuum.

Given:

By=(3.5×10−7)sin⁡(1.5×103x+0.5×1011t) TB_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:

Ez=cBy=(3×108)(3.5×10−7) V/m=105 V/m.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:

Ez=105sin⁡(1.5×103x+0.5×1011t) V/m.E_z = 105 \sin (1.5 \times 10^3 x + 0.5 \times 10^{11} t) \, \text{V/m}.