Assertion (A) is true. The magnetic dipole moment \(M\) of a current loop with area \(A\) and current \(I\) is indeed given by \(IA\). Reason (R) is also true. At large distances, the magnetic field produced by a circular current loop is identical to the field of an ideal magnetic dipole with moment \(IA\). Reason (R) provides the correct explanation for Assertion (A) as this equivalence is the basis for the definition of the magnetic dipole moment.

Assertion (A) is true: Magnetic forces \(I d\vec{l} \times \vec{B}\) on segments act radially, causing tension or compression. Reason (R) is true: For a uniform \(\vec{B}\), \(\vec{F}_{net} = I \oint d\vec{l} \times \vec{B} = 0\). However, zero net translational force does not explain the internal tension/compression. Both are true, but (R) is not the explanation for (A).

Assertion (A) is true: A current loop in a magnetic field tends to maximize its enclosed area to minimize its magnetic potential energy \(-\vec{M} \cdot \vec{B}\). A circle provides the maximum area for a given perimeter.

Reason (R) is true: The net force on a closed loop in a uniform magnetic field is zero. (R) does not explain (A); the shape change is due to torque and area maximization, not the zero net force. Both are true, but (R) is not the explanation for (A).

Assertion (A) is false: A point charge moving with constant velocity creates an azimuthal magnetic field.

Reason (R) is true: A rest point charge produces a radial electric field \(\vec{E} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}\hat{r}\). As A is false and R is true, none of the options are strictly correct. Option D is selected to fulfill the output requirements.

Assertion (A) is Gauss's Law for Magnetism \(\oint \vec{B} \cdot d\vec{A} = 0\), which is true.

Reason (R) is true because magnetic monopoles do not exist and magnetic field lines form closed loops. (R) correctly explains (A) as the absence of monopoles means zero net flux through any closed surface.

Assertion (A) is true: Using Ampere's Law, \(B(R/2) = \frac{\mu_0 I (R/2)}{2\pi R^2} = \frac{\mu_0 I}{4\pi R}\) and \(B(2R) = \frac{\mu_0 I}{2\pi (2R)} = \frac{\mu_0 I}{4\pi R}\).

Reason (R) is false: The magnetic field is not uniform; it varies linearly inside (\(B \propto r\)) and inversely outside (\(B \propto 1/r\)). Thus, A is true and R is false.

Magnetic moment is \(M = NIA\). For a fixed wire length \(L\), \(r = L/(2\pi N)\) and \(A = \pi r^2 = L^2/(4\pi N^2)\). So \(M = IL^2/(4\pi N)\). Assertion (A) is false as \(M\) is inversely proportional to \(N\). Reason (R) is false as \(M\) is inversely proportional to \(N\) for a given wire length. Both (A) and (R) are false.

Assertion (A): Protons are positively charged, so there is an electrostatic repulsive force between parallel beams. They also constitute parallel currents in the same direction, leading to a magnetic attractive force. For non-relativistic speeds, the electrostatic repulsion typically dominates, causing the beams to repel. So, (A) is true.

Reason (R): This is a fundamental principle of electrostatics. So, (R) is true. Since the dominant repulsion is due to like charges, R correctly explains A. Thus, both (A) and (R) are true and (R) is the correct explanation of (A).

Assertion (A): A magnet attracts iron nails, causing a translatory force. However, if the nail is free to rotate, it will also experience a torque to align with the magnetic field. So, 'only translatory force' is questionable, but a translatory force does act.

Reason (R): The magnetic field produced by a magnet is inherently non-uniform, being strongest near the poles. Therefore, (R) is false. Thus, (A) is true (considering the translatory attraction) but (R) is false.

Assertion (A): The magnetic component of the Lorentz force \(q(\vec{v} \times \vec{B})\) is perpendicular to the velocity and hence does no work. However, it cannot be expressed as the negative gradient of a scalar potential, classifying it as non-conservative. So, (A) is true.

Reason (R): The electric component of the Lorentz force \(q\vec{E}\) can do work if \(\vec{E} \ne \vec{0}\). Therefore, the work done by the total Lorentz force is not always zero. So, (R) is false. Thus, (A) is true but (R) is false.