Expression for the electric field is (a) Ey=60 sin(0.5 ×10^3 x+1.5 ×10^11 t] Vm^-1 (b) Ey=600 si

step 1 From this given magnetic field equation we can say that the wave propagation propagation is in x

Expression for the electric field is (a) Ey=60 sin(0.5 ×10^3...

Expression for the electric field is (a) $E_{y}=60 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right] \mathrm{Vm}^{-1}$ (b) $E_{y}=600 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}$ (c) $E_{2}=60 \sin \left(0.5 \times 10^{7} x+1.5 \times 10^{11} t\right] \mathrm{Vm}^{-1}$ (d) $E_{4}=600 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}$

Expression for the electric field is
(a) $E_{y}=60 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right] \mathrm{Vm}^{-1}$
(b) $E_{y}=600 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}$
(c) $E_{2}=60 \sin \left(0.5 \times 10^{7} x+1.5 \times 10^{11} t\right] \mathrm{Vm}^{-1}$
(d) $E_{4}=600 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}$

Key Concepts

Electromagnetic Wave

An electromagnetic wave is characterized by oscillating electric and magnetic fields that propagate through space. The electric field in such a wave is typically expressed as a sinusoidal function, capturing both its spatial and temporal variations, which are governed by the principles of Maxwell's equations.

Sinusoidal Wave Representation

A sinusoidal function, such as a sine or cosine, is used to mathematically represent periodic oscillations in physical systems. In the context of electromagnetic waves, it encapsulates the periodic variation of the electric field with respect to space and time, where the argument of the sine function represents the phase of the wave.

Wave Parameters

Key parameters in a sinusoidal wave expression include the amplitude, wavenumber, and angular frequency. The amplitude defines the peak value of the electric field, the wavenumber relates to the spatial frequency (or the inverse of the wavelength), and the angular frequency determines the rate of oscillation in time. Together, these parameters fully describe the wave's behavior.

Dimensional Consistency and Units

Ensuring that an expression for the electric field is dimensionally consistent is essential. The amplitude must carry the correct units (typically volts per meter for an electric field), and the arguments of the trigonometric functions must be dimensionless, requiring proper matching of the units in the spatial and temporal terms.

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