Electromagnetic Waves

Typically, television broadcasting signals utilize frequencies within the range of 30-300 MHz. TV and radar transmissions commonly employ the VHF (Very High Frequency) band, which spans from 30 MHz to 300 MHz.

1. Radius of Circular Path:
The magnetic force ( ) on a charged particle is given by:
This force provides the centripetal force ( ):
Equating the two forces:
Solving for the radius (r):
2. Radii for the Two Particles:
Radius for particle 1 ( ):
Radius for particle 2 ( ):
3. Maximum Separation:
The maximum separation ( ) between the particles will occur when they complete a half-circle (a semicircle).
The separation will be the difference in the diameters of their circular paths.
Diameter of particle 1:
Diameter of particle 2:
Maximum separation ( ) =

Therefore, the maximum separation of the particles is , which matches option (3).

We are given:
- Current ,
- Magnetic field ,
- The direction of the current is from south to north.
The force per unit length on a current-carrying conductor placed in a magnetic field is given by the formula: where: - is the magnetic field, - is the current, - is the angle between the direction of the current and the magnetic field. Step 1: Analyze the Direction of the Magnetic Field and the Current In this case, the direction of the current is from south to north, and the horizontal component of the magnetic field is also in the horizontal plane. The force is calculated based on the angle between the magnetic field and the current direction.
Since the magnetic field is horizontal and the current is also horizontal, and both are in the same plane, the angle between the current and the magnetic field is (as the two vectors are parallel).
Step 2: Apply the Formula Substituting into the equation:
Thus, the force per unit length on the conductor is zero.
Conclusion: The force per unit length on the conductor is zero, so the correct answer is Option (2).

The electric field for an electromagnetic wave is given as: Where:
is the magnitude of the electric field,
is the wave vector,
is the angular frequency.
The wave number is related to the angular frequency by the equation: Where is the speed of light. Substituting the values:
Final Answer: 2 rad/m.

Electromagnetic waves are produced by accelerating charges. This is a fundamental concept in electromagnetism, where oscillating or accelerating charges generate time-varying electric and magnetic fields that propagate through space as electromagnetic waves.
Step 1: When charges are stationary, they produce electric fields, but no magnetic field, hence they do not generate electromagnetic waves.
Step 2: Charges in uniform motion create a constant magnetic field and may generate electromagnetic radiation if they are moving in a changing manner, but only accelerating charges produce the full electromagnetic wave.
Step 3: The correct answer is that accelerating charges produce electromagnetic waves as described by Maxwell's equations.

We are given:
- The refractive index of the medium, ,
- The relative permeability of the medium, .
The refractive index is related to the relative permittivity and the relative permeability by the formula:
where:
- is the relative permittivity,
- is the relative permeability.
Substitute the given values into this equation: Squaring both sides:
Now, solving for : Thus, the relative permittivity of the medium is approximately .
Conclusion: The relative permittivity of the medium is nearly 1.5, so the correct answer is Option (1).

The voltage gain ( ) of the common emitter amplifier is given as . The input resistance is given as .
The output resistance is given as . The power gain ( ) of an amplifier is the ratio of the output power to the input power: We can express power in terms of voltage and resistance, . Thus, Substituting these into the power gain equation: We know that voltage gain . Therefore, Substituting the given values: The power gain of the amplifier is 1800.
Correct Answer: (4) 1800

The emf induced in a rotating conductor in a magnetic field is given by where is the magnetic field strength, is the angular velocity, is the frequency, and is the length of the conductor.
In this case, we are given that , , and , so

Step 1: Convert mutual inductance to Henrys. Mutual inductance .
Step 2: Calculate the change in current. The current change .
Step 3: Calculate the change in flux linked with the other coil.

Step 1: Understanding the EM Wave Propagation For an electromagnetic wave propagating in the positive Z-direction: The electric field is perpendicular to the direction of propagation.
The magnetic field is also perpendicular to the propagation.
and the direction of propagation (Z) should form a right-handed coordinate system.
Step 2: Check the Cross Product Rule Verifying for the given vectors: yields a component in the -direction, confirming the correct orientation.