Download App

Electromagnetic Waves — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Waves5 Marks
Question
A plane electromagnetic wave is passing through a region. Consider (a) electric field (b) magnetic field (c) electrical energy in a small volume and (d) magnetic energy in a small volume. Construct the pairs of the quantities that oscillate with equal frequencies.
✓

Answer

Let the electromagnetic wave be propagating in the z-direction. The vibrations of the electric and magnetic fields are given by,
$\text{E}_\text{x}=\text{E}_0\sin(\text{kz}-\omega\text{t})$
$\text{B}_\text{y}=\text{B}_0\sin(\text{kz}-\omega\text{t})$
Let the volume of the region be V.
The angular frequency of the vibrations of the electric and magnetic fields are same and are equal to $\omega$
Therefore, their frequency, $\text{f}=\frac{\omega}{2\pi},$ is same.
The electrical energy in the region,
$\text{U}_\text{E}=\Big(\frac{1}{2}\in_0\text{E}^2\Big)\times\text{V}$
It can be written as,
$\text{U}_\text{E}=\Big(\frac{1}{2}\in_0\big(\text{E}^2_0\sin^2(\text{kz}-\omega\text{t})\big)\Big)\times\text{V}$
$\text{U}_\text{E}=\Bigg(\frac{1}{2}\in_0\text{E}_0^2\times\frac{\big(1-\cos2(\text{kz}-\omega\text{t})\big)}{2}\Bigg)\times\text{V}$
$\text{U}_\text{E}=\Big(\frac{1}{4}\in_0\text{E}_0^2\times(1-\cos2(\text{kz}-\omega\text{t}))\Big)\times\text{V}$
The magnetic energy in the region,
$\text{U}_\text{B}=\Big(\frac{\text{B}^2}{2\mu_0}\Big)\times\text{V}$
$\text{U}_\text{B}=\bigg(\frac{\text{B}^2_0\sin^2(\text{kz}-\omega\text{t})}{2\mu_0}\bigg)\times\text{V}$
$\text{U}_\text{B}=\Bigg(\frac{\text{B}^2_0\big(1-\cos(2\text{kz}-2\omega\text{t})\big)}{4\mu_0}\Bigg)\times\text{V}$
The angular frequency of the electric and magnetic is same and is equal to $2\omega$
Therefore, their frequency,
$\text{f}'=\frac{2\omega}{2\pi}=2\text{f}$
Will be same.
Thus, the electric and magnetic fields have same frequencies and the electrical and magnetic energies will have same frequencies.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Electromagnetic Waves→Electromagnetic Waves — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Two small balls, each of mass m are connected by a light rigid rod of length L. The system is suspended from its centre by a thin wire of torsional constant k. The rod is rotated about the wire through an angle $\theta_0$ and released. Find the tension in the rod' as the system passes through the mean position.
→
The plates of a capacitor are 2.00cm apart. An electronproton pair is released somewhere in the gap between the plates and it is found that the proton reaches the negative plate at the same time as the electron reaches the positive plate. At what distance from the negative plate was the pair released?
→
Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of (i) electric dipole p in an electrostatic field E and (ii) magnetic dipole m in a magnetic field B. Write down a set of conditions on E, B, p, m so that the two motions are verified to be identical. (Assume identical initial conditions.)
→
Write the truth table for the circuit shown in Fig. Name the gate that the circuit resembles.
→
Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line intergral $\Im(\text{L})=\begin{vmatrix}\int\limits_{-\text{L}}^{\text{L}}\text{B.dl} \end{vmatrix}$ taken along z-axis.
  1. Show that $\Im(\text{L})$ monotonically increases with L.
  2. Use an appropriate Amperian loop to show that $\Im(\infty)=\mu_0\text{I}$, where I is the current in the wire.
  3. Verify directly the above result.
  4. Suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about $\Im(\text{L})$ and $\Im(\infty)$?
→
  1. A point object is placed on the principal axis of a convex spherical surface of radius of curvature R, which separates the two media of refractive indices $n_1$ and $n_2(n_2 > n_1)$. Draw the ray diagram and deduce the relation between the object distance (u), image distance (v) and the radius of curvature (R) for refraction to take place at the convex spherical surface from rarer to denser medium.
  2. A converging lens has a focal length of 20 cm in air. It is made of a material of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length.
→
A capacitor of capacitance C is connected to a battery of emf $\in$ at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?
→
A spherical capacitor has an inner sphere of radius 12cm and an outer sphere of radius 13cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
  1. Determine the capacitance of the capacitor.
  2. What is the potential of the inner sphere?
  3. Compare the capacitance of this capacitor with that of an isolated sphere of radius 12cm. Explain why the latter is much smaller.
→
Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x << R, find the time period of oscillation of the particle if it is released from there.
→
In beta decay, an electron (or a positron) is emitted by a nucleus. Does the remaining atom get oppositely charged?
→