Physics

The direction of the vector (cross) product is determined by the right-hand rule, which states that if you point your right hand's fingers along the first vector and curl them towards the second vector, your thumb points in the direction of the cross product.

The torque $\tau$ on a rectangular coil carrying current $I$ with $N$ turns, area $A$, in a magnetic field $B$ is given by $\tau =NIAB\sin \varphi$, where $\varphi$ is the angle between the normal to the plane of the coil and the magnetic field. When the plane of the coil is parallel to the magnetic field, the normal to the coil is perpendicular to the field, so $\varphi =90^{\circ }$ and $\sin 90^{\circ }=1$. Thus, the torque is maximum and equals $\tau =NIAB$. The formula involving cosine is incorrect for torque; it is the sine of the angle that determines the torque magnitude. Therefore, the correct general formula is $\tau =NIAB\sin \varphi$ (option B).

Torque and energy both have the same dimensional formula M L² T⁻². Momentum and impulse both have dimensions M L T⁻¹. Energy and work have identical dimensions M L² T⁻². Mass has dimension M, while moment of inertia has dimension M L². Therefore, the pair that does not have identical dimensions is mass and moment of inertia, making option D the correct answer.

The sensitivity of a moving coil galvanometer is increased by increasing the number of turns in the coil, which increases the magnetic torque for a given current, thereby producing a larger deflection. While a stronger magnetic field also affects sensitivity, increasing the number of turns is a more direct and commonly used method.

In a multi-range ammeter, the meter movement has a fixed full-scale deflection current and internal resistance. To measure higher currents (increase the range), shunt resistors are connected in parallel with the meter coil to bypass most of the current. As the range increases, the shunt resistor value decreases to allow more current to bypass the meter coil, protecting it from damage. Therefore, the shunt value decreases as the range increases.

For three coplanar forces to keep a body in equilibrium, they must be concurrent, meaning their lines of action intersect at a single point. This ensures the net force and net moment are zero, satisfying equilibrium conditions.

A voltmeter is designed to measure the potential difference (voltage) across two points without drawing any significant current from the circuit, ensuring accurate voltage measurement. Other instruments like ammeters draw current, and galvanometers measure current, while CROs display voltage waveforms but are not primarily used to measure potential without current draw.

The root mean square (r.m.s) current is defined as the steady current that produces the same heating effect in a resistor as the alternating current. This is because the r.m.s value represents the effective value of the AC current in terms of power dissipation.

An ammeter is connected in series with the circuit so that it measures the total current flowing through that part of the circuit. Connecting it in parallel would not measure the total current and could damage the meter.

Electromagnetic waves carry energy as they propagate through space. They also carry momentum, but the primary and most direct transport property is energy. They do not carry mass or heat themselves.