Torque On A Current Loop

A current loop in a uniform field experiences a torque $\tau =NIAB\sin \theta$, where $\theta$ is the angle between the magnetic moment (the normal to the coil plane) and the field. When the plane of the coil is parallel to the field, the normal is perpendicular to the field, so $\theta =90^{\circ }$ and $\sin \theta =1$, giving maximum torque. Substituting $N=20$, $I=4\text{A}$, $A=0.05{\text{m}}^2$ and $B=0.3\text{T}$, we get $\tau =(20)(4)(0.05)(0.3)(1)=1.2\text{N m}$. The option $0.6\text{N m}$ wrongly inserts $\sin 45^{\circ }$ or halves a factor. The option $0\text{N m}$ would apply only if the plane were perpendicular to the field, where the normal aligns with $B$. The option $2.4\text{N m}$ doubles the turns. This is the operating principle of the moving-coil galvanometer in NCERT. A sanity check confirms newton-metre units and that the torque is greatest precisely when the plane lies along the field. The same physics underlies every electric motor: the torque tends to rotate the coil until its magnetic moment aligns with the field, and a commutator reverses the current each half-turn to keep the rotation continuous. In a galvanometer, by contrast, a spiral spring supplies a restoring torque so the coil settles at a deflection proportional to current, converting the rotational tendency described here into a steady, readable measurement of current.