Electricity and Magnetism

At absolute zero (0 K), the thermal vibrations of atoms in a conductor cease, causing the resistance to drop to nearly zero. This is because resistance in conductors primarily arises from lattice vibrations, which are absent at absolute zero.

In metallic conductors, electric current is primarily due to the flow of free electrons, which are negatively charged particles that move through the metal lattice when a potential difference is applied. Protons and neutrons do not move freely in a conductor, and the mechanism is well established, so it is not under controversy.

A fuse is designed to protect electrical circuits by breaking the circuit when the current exceeds a safe level, thus preventing damage from high current. It does not directly protect against high voltage or overheating, although it indirectly prevents overheating by stopping excessive current.

The resistance of a conductor depends on the nature of the conductor (material), its dimensions (length and cross-sectional area), and its physical state (such as temperature). Therefore, all the given factors affect resistance.

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, resulting in a straight line when voltage is plotted against current on a graph.

Copper is the best material for making connecting wires because it has excellent electrical conductivity, is relatively inexpensive, and is ductile, making it easy to draw into wires. While silver has slightly better conductivity, it is much more expensive and less commonly used for wiring.

Tungsten is used for bulb filaments because it has a very high melting point and good electrical resistance, making it ideal for glowing brightly without melting. The other materials either have lower melting points or are not suitable for filament use.

The energy required to magnetize and demagnetize a material is represented by the area of the hysteresis loop. This area corresponds to the energy loss per cycle due to magnetic hysteresis.

A ferromagnet becomes fully magnetized when subjected to a direct current (D.C.) at its peak value, as this provides a steady magnetic field that aligns the magnetic domains. Alternating current (A.C.) continuously changes direction, preventing full magnetization.

When two protons are brought closer, the electrostatic repulsive potential energy between them increases because like charges repel each other, raising their potential energy.

The Curie temperature is the temperature at which a ferromagnetic material loses its permanent magnetic properties and becomes paramagnetic due to thermal agitation overcoming magnetic ordering.

The magnetic force per unit positive charge moving perpendicular to the magnetic field with unit velocity defines the magnetic field intensity (also called magnetic field strength). Magnetic induction refers to the magnetic flux density, which is related but not the force per unit charge and velocity.

Materials where valence electrons are tightly bound to their atoms at low temperatures do not allow free movement of electrons, making them insulators. This restricts electrical conductivity, distinguishing them from conductors and semiconductors.

A magnetometer is an instrument specifically designed to detect and measure very weak magnetic fields, making it the correct choice. Squids are animals, MRI is a medical imaging technique that uses magnetic fields but does not detect weak fields externally, and an oscilloscope measures electrical signals, not magnetic fields.

Coercive force is the magnetic field strength required to reduce the magnetization of a material to zero after it has been magnetized; thus, it opposes demagnetization.

Electrons in the conduction band are free to move and thus can transport electric charge, which is the fundamental principle behind electrical conductivity in materials.

The cutoff frequency (also called the -3dB frequency) of an RC circuit is given by the formula f = 1/(2πRC). Among the given options, the closest correct formula is 1/(2RC), which is option D. The exact formula includes 2π in the denominator, so none of the options perfectly match the exact formula, but option D is the closest and most correct approximation compared to the others.

The root mean square (r.m.s) value of an alternating current is defined as the square root of the mean (average) of the square of the instantaneous current values over one complete cycle. This matches option B.

The permeability of free space (also called the magnetic constant) is exactly 4π × 10⁻⁷ henry per meter (H/m), which is equivalent to Wb·A⁻¹·m⁻¹ in SI units. This value is fundamental in electromagnetism.

Magnetic flux (Φ) is defined as the product of the magnetic flux density (B) and the area (A) through which the field lines pass, so Φ = B × A. This relationship directly connects the two quantities.

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.

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.

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.

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).

In a pure resistor circuit, the voltage and current are in phase, meaning they have zero phase difference. This means the voltage and current reach their maximum and zero values simultaneously.