Question

Consider an electromagnetic wave propagating in a vacuum. Choose the correct statement :
A) for an electromagnetic wave propagating in +y direction, the 1A electric field is $E=\dfrac{1}{\sqrt{2}}{{E}_{yz}}(x,t)\hat{z}$ and the magnetic field is $B=\dfrac{1}{\sqrt{2}}{{B}_{x}}(x,t)\hat{y}$
B) for an electromagnetic wave propagating in +y direction, the 1A electric field is
$E=\dfrac{1}{\sqrt{2}}{{E}_{yz}}(x,t)\hat{y}$and the magnetic field is $B=\dfrac{1}{\sqrt{2}}{{B}_{x}}(x,t)\hat{z}$
C) for an electromagnetic wave propagating in +x direction, the 1A electric field is
\[E=\dfrac{1}{\sqrt{2}}{{E}_{yz}}(x,t)(\hat{y}-\hat{z})\] and the magnetic field is $B=\dfrac{1}{\sqrt{2}}{{B}_{yz}}(x,t)(\hat{y}+\hat{z})$
D) None

Answer 1

Hint: In any electromagnetic wave, the angle between the electric field and the magnetic field will be equal to ninety degrees. The direction of propagation of the component of electric and magnetic fields will be in the y-z plane. Therefore, with the above information, we can guess the function of the electromagnetic wave.

Complete step-by-step solution:
In any electromagnetic wave, the angle between the magnetic field and the electric field will be ninety degrees as told earlier and can be seen in the following diagram:

Also, if the wave is assumed to be propagated in the x-direction, the function of both the electric field and the magnetic field will be in x at time t. If so in the y-direction, the component will be in y and time t.
Next, if it is assumed in the x-direction, the component of the electric field and magnetic field will be in the y-z plane. So, let's now solve the options one at a time and find the correction e.
In the first option, the function of a wave propagating in the y-direction is taken as x and time t, hence option a is incorrect.
In option b, the function of the wave propagating in the y-direction is taken as x and time t, hence option b is incorrect.
In option c, the wave is propagating in the x-direction, the function is in terms of x and time t and also, the component of electric and magnetic fields is in the y-z plane. Therefore, it satisfies all the conditions.
Hence, option (C) is the correct option.

Note: One of the components of the electric field and magnetic field will be in the y-z plane if the wave is propagating in the x-direction. Also, the function of the electromagnetic wave in electric fields and magnetic fields will depend on the direction in which the wave is propagating. Take care while solving such typical formulas.