Electromagnetism

Step 1: Analyze Assertion (A).
Electromagnetic (EM) waves consist of oscillating electric and magnetic fields that can propagate through a vacuum, as described by Maxwell’s equations. Unlike mechanical waves, which require a medium, EM waves do not need a medium to travel (e.g., light travels through space). Thus, Assertion (A) is true. Step 2: Analyze Reason (R).
EM waves are transverse waves because their electric and magnetic fields oscillate perpendicular to the direction of propagation. For example, if an EM wave propagates along the -axis, the electric field may oscillate along the -axis and the magnetic field along the -axis. This is a defining characteristic of EM waves, so Reason (R) is true. Step 3: Check if Reason (R) explains Assertion (A).
The ability of EM waves to propagate without a medium is due to their nature as self-sustaining oscillations of electric and magnetic fields, not because they are transverse. Mechanical transverse waves (e.g., on a string) require a medium, showing that being transverse does not imply no medium is needed. Thus, while both statements are true, Reason (R) does not explain Assertion (A). Step 4: Conclusion.
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A), so the correct option is (B).

Step 1: Analyze Assertion (A).
The velocity of the particle is , and the magnetic field is . The magnetic force is: The force is along the -axis. The velocity component perpendicular to ( ) causes circular motion in the - plane, while the component parallel to ( ) causes linear motion along the -axis. This results in a helical path with the axis along the -axis, not the -axis as stated. Thus, Assertion (A) is false. Step 2: Analyze Reason (R).
The magnetic force is perpendicular to the velocity , not along it, unless , which is not the case here. Thus, Reason (R) is false. Step 3: Conclusion.
Since both Assertion (A) and Reason (R) are false, the correct option is (D).

Step 1: Understand the magnetic flux formula.
The magnetic flux through a coil is given by: where is the magnetic field, is the area vector of the coil, and the dot product accounts for the angle between them. Step 2: Determine the angle between and .
The area vector is perpendicular to the plane of the coil, with magnitude . The problem states that the plane of the coil makes an angle with . Therefore, the angle between and the normal to the plane (i.e., ) is: Step 3: Compute the magnetic flux.
The dot product is: Substitute : However, we need to interpret the angle correctly. If the plane of the coil makes an angle with , the angle between and the normal to the plane is (if is defined as the angle between the field and the plane). Thus: But in standard physics, the angle given is often between and the normal to the plane. Let’s correct our interpretation: if the plane makes an angle with , the normal to the plane makes an angle with , but typically, the angle in such problems is between and the normal. So, if is the angle between and the normal: Step 4: Match with the options.
The flux is , which matches option (B).

(a): Differentiate between conduction and displacement current.
- Conduction Current: This is the current due to the actual movement of charges (e.g., electrons) in a conductor, such as in a wire. It occurs in materials with free charges.
- Displacement Current: Introduced by Maxwell, this is a time-varying electric field that produces a magnetic field, even without charge movement. It exists in regions like the gap of a charging capacitor.
- Similarity: Both contribute to the magnetic field, as per the Ampere-Maxwell law: .
- Dissimilarity: Conduction current involves the physical movement of charges, while displacement current arises from a changing electric field without charge movement. (b): Electromagnetic waves in free space.
Displacement current enables electromagnetic waves in free space by ensuring continuity in Maxwell’s equations. In a vacuum, there is no conduction current, but a changing electric field creates a displacement current: where is the electric flux. For example, an oscillating charge produces a varying electric field, leading to a displacement current. This displacement current generates a magnetic field, which in turn induces a changing electric field. This self-sustaining process results in the propagation of electromagnetic waves in free space.