Physics

The vectors $\mathbf{i},\mathbf{j},\mathbf{k}$ are unit vectors along the x, y, and z axes respectively. The cross product $\mathbf{j}\times \mathbf{k}=\mathbf{i}$, which is a unit vector. The dot product $\mathbf{i}\cdot \mathbf{i}=1$, so the magnitude is 1.

In a radial magnetic field, the coil of a galvanometer is positioned so that the magnetic field lines are always radial to the coil's rotation axis. This arrangement ensures that the angle between the coil plane and the magnetic field is always 90°, making the deflecting torque proportional to BINA sinα, where α = 90°, so sinα = 1. Therefore, the torque is always BINA sin90° = BINA, meaning the torque depends on BINA sinα. Hence, the correct expression is BINA sinα.

The cross product of the unit vectors $\hat{i}$ and $\hat{j}$ is $\hat{k}$, following the right-hand rule in vector algebra.

The question asks for the minimum current required to produce a 1 mm deflection at 1 meter distance, which corresponds to the current sensitivity of the galvanometer, typically expressed in milliamperes (mA). Among the options, '1 m A' (1 milliampere) is the correct numerical value representing this minimum current. Option C, 'current sensitivity,' is a concept, not a numerical value, so it cannot be the correct answer here.

When a capacitor of capacitance C is charged by a constant current I, the voltage V across the capacitor increases linearly with time t according to the formula V = (I/C) * t. Rearranging for time, t = (C * V) / I. Substituting the given values: C = 30 µF = 30 × 10⁻⁶ F, V = 300 V, and I = 10 mA = 10 × 10⁻³ A, we get t = (30 × 10⁻⁶ F * 300 V) / (10 × 10⁻³ A) = 0.9 seconds. Therefore, the time taken for the potential difference to reach 300 V is 0.9 seconds, which corresponds to option A.

An inductor stores energy in its magnetic field created by the current flowing through its coils. It does not store energy in an electric field.

A magnetic compass needle aligns with magnetic fields, which are produced by moving charges (currents). A charge at rest does not produce a magnetic field, so only a charge in motion can deflect the compass needle.

When a current-carrying conductor is placed in a magnetic field parallel to it, the angle θ between the conductor and the magnetic field is 0°. The magnetic force is given by F = BIL sinθ. Since sin0° = 0, the force experienced by the conductor is zero.

Electromagnetic waves emitted from an antenna are transverse waves because their oscillations are perpendicular to the direction of wave propagation. They are not stationary or longitudinal waves.

The greatest accuracy in measuring unknown resistance using a slide wire bridge is achieved when the balance point is near the middle of the wire. This ensures that the lengths on either side are nearly equal, minimizing errors due to wire non-uniformity and maximizing measurement precision.