Electromagnetic Waves

So, the correct option is (A): 2.2 A

To find the impedance of the LCR series circuit, let's go through the given information and use relevant formulas.

The LCR series circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series with an AC source of potential difference volts. The potential differences across L, C, and R are given as:

• Potential difference across the inductor  
• Potential difference across the capacitor
• Potential difference across the resistor

The amplitude of the current flowing through the circuit is .

The impedance of the LCR circuit is calculated using:

where is the inductive reactance and is the capacitive reactance.

The total potential difference in the circuit using impedance can be expressed as:

We can calculate the total voltage:

Substituting the given values, we get:

Now, using the formula , we substitute the known values:

Hence, the impedance of the circuit is , which is the correct answer.

To solve this problem, we need to understand how electromagnetic waves propagate. For a plane electromagnetic wave traveling in the -direction, the directions of the electric field ( ) and magnetic field ( ) should be perpendicular to each other and also perpendicular to the direction of propagation. This is described by the right-hand rule, as well as being consistent with Maxwell's equations.

1. The wave is propagating in the -direction. Therefore, the and fields must lay in the -plane (perpendicular to ).
2. The options for the directions of and are given:
3. We apply the right-hand rule: if you point the thumb of your right hand in the direction of the wave propagation (i.e., -direction), and your fingers in the direction of the electric field ( ), your palm points in the direction of the magnetic field ( ), or vice versa.
4. Analyzing the directions:
   • for implies the field is in the negative -direction and positive -direction.
   • for implies the field is in the negative -direction and negative -direction.
5. This orientation aligns with the perpendicular requirement and satisfies Maxwell’s equation constraints based on the given direction of wave propagation.
6. Consequently, the correct option is , where both fields are perpendicular to the direction of wave propagation and each other. This also means that the curl of aligns properly with , confirming this is a valid electromagnetic wave arrangement traveling in the x-direction.

To solve this problem, we need to understand the properties of electromagnetic waves (EM waves). In a plane electromagnetic wave, the electric field ( ) and the magnetic field ( ) are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.

For a plane electromagnetic wave propagating in the -direction, the direction of these fields can be determined by the following rules:

• The electric field ( ) is always perpendicular to the direction of wave propagation.
• The magnetic field ( ) is also perpendicular to the direction of wave propagation and to the electric field.
• The direction of propagation of the wave is given by the cross product .

Let's consider each option to see which fits these criteria:

1. : This option suggests both fields are in the same plane, which would violate the perpendicularity criterion.
2. : Again, both fields point in the same general direction, which is not possible because they should be perpendicular to each other.
3. : In this combination, the electric field could be in the direction, while the magnetic field is in the perpendicular plane, maintaining perpendicularity to the wave direction and to each other.
4. : This setup does suggest different planes, but does not align correctly as the cross product would not give a clear direction which is necessary for propagation in the -direction.

Therefore, the correct choice is option three, , where the electric field and magnetic field are correctly oriented such that their cross product results in the propagation along the -direction.

We can match List-I and List-II as follows:

• AM radio waves have a wavelength of 10² m, which is comparatively longer, typical for radio waves.
• Microwaves have a wavelength of 10^-2 m, suitable for applications like cooking in microwave ovens.
• Infrared radiations have shorter wavelengths, but let's consider the longest option available in the context, so we'll skip this for now to explore shorter.
• X-rays are known to have very short wavelengths like 10^-10 m.

The correct matching based on wavelength is:

• AM radio waves: 10² m
• Microwaves: 10^-2 m
• Infrared Radiations (assuming a typo with available options): not specifically matching but should be shortest, however, choosing next shortest for completion under constraints
• X-rays: 10^-10 m

Thus, the correct answer is: (a) - (ii), (b) - (iii), (c)-(iv), (d) - (i)

1. Electromagnetic waves are transverse in nature. This means that the electric and magnetic fields oscillate perpendicular to the direction of wave propagation.
2. The energy density in the electric field is indeed equal to the energy density in the magnetic field for these waves. The energy (U) is given as , where is the electric field, is the magnetic field, is the permittivity of free space, and is the permeability of free space.
3. They travel with a speed , known as the speed of light in free space, approximately m/s.
4. Electromagnetic waves do not originate from charges moving with uniform speed. Instead, they are produced by accelerated charges or time-varying currents. This property is the correct answer because charges moving with constant (uniform) speed do not produce changing electromagnetic fields.