Correct Option: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Step 1 (Governing Law & Formula): [0.5 Mark]

The torque $\vec{\tau}$ experienced by a current-carrying coil placed in a magnetic field $\vec{B}$ is given by:

$$\vec{\tau} = \vec{m} \times \vec{B}$$

Where $\vec{m} = NIA$ is the magnetic dipole moment. In a radial magnetic field, the plane of the coil is always parallel to the magnetic field lines, ensuring the angle $\theta$ between the area vector and the magnetic field is always $90^\circ$.

Step 2 (Mathematical Working): [0.25 Mark]

The magnitude of the deflecting torque is:

$$\tau = NIAB \sin(90^\circ) = NIAB$$

This deflecting torque is balanced by the restoring torque of the spring, $\tau_{restoring} = k\phi$, where $k$ is the torsional constant and $\phi$ is the angle of deflection. Equating the two:

$$k\phi = NIAB$$ $$\phi = \left( \frac{NAB}{k} \right) I$$

Step 3 (Final Concluded Answer): [0.25 Mark]

Since $N, A, B,$ and $k$ are constants for a given galvanometer, we have $\phi \propto I$. Thus, the deflection is directly proportional to the current, which is made possible specifically by the use of a radial magnetic field that keeps the torque independent of the coil's orientation.

💡 EL10 Concept Insight: Imagine the coil is like a spinning door; a radial magnetic field acts like a constant breeze pushing the door from the side no matter which way it turns, ensuring the push is always perfectly proportional to the strength of the current.