Solution:

Ans. When the motion of the charge accelerates, then there will be change in electric and magnetic fields with respect to space and time which generates electromagnetic waves. So we see that an accelerated charge will give electromagnetic waves. In an oscillatory $L-C$ circuit, a charge oscillates across the capacitor plates. This oscillating charge has a non-zero acceleration, hence it emits electromagnetic waves of frequency same as that of the oscillating charge.

The figure shows the graphical representation of an electromagnetic wave where the electric field vector $\vec{E}$ and the magnetic field vector $\vec{B}$ are vibrating along $Y$ and $X$-directions respectively, and the wave is propagating along Z-direction. Both $\vec{E}$ and $\vec{B}$ vary with time and space and have the same frequency.

[as $(E \hat{j} \times B \hat{k})=-E B \hat{i}$ ]

Direction of Propagation :

Envelope of $\vec{B}$ AT Q. 10. (i) An EM wave is travelling in a medium with a velocity $\vec{v}=v \hat{i}$. Draw a sketch showing the propagation of the EM wave, indicating the direction of the oscillating electric and magnetic fields.

(ii) How are the magnitudes of the electric and magnetic fields related to the velocity of the EM wave?

U [Delhi I, II, III 2013]

Ans. (i)

(ii)

[CBSE Marking Scheme 2013]

Detailed Answer:

(i) In the figure, $\vec{E} \times \vec{B}$ shows the direction of the

propagation of the electromagnetic wave where direction of oscillating field is

$$ \hat{i}=\hat{j} \times \hat{k} $$

Direction of Propagation :

Envelope of $\overrightarrow{\mathrm{E}}$

(ii) As seen, velocity of the light is equal to the ratio of the magnitude of the electric and magnetic field vectors. Apart from electric field vector, magnetic field vector and light propagation vector forms a perpendicular triad, hence speed of electromagnetic wave

$$ c=\left|\frac{E_{0}}{B_{0}}\right| $$