Electricity and Magnetism

When two identical conducting spheres are connected by a wire, charges redistribute equally. Initially, charges are +2Q and -Q, total charge is +Q. After connection, each sphere has charge +Q/2. The force depends on the product of charges, so new force F' = k*(Q/2)*(Q/2)/r^2 = k*Q^2/4r^2, which is one-fourth the original force F. Hence, the force becomes F/4.

Gamma rays are electromagnetic radiation and have no charge, so they are not deflected by electric or magnetic fields. Alpha and beta rays are charged particles and are deflected accordingly.

In semiconductors, electrical conductivity increases with temperature because more charge carriers are generated as temperature rises. In contrast, conductors typically show decreased conductivity with increasing temperature due to increased lattice vibrations.

The core of a transformer is laminated to reduce eddy current losses. Laminations increase the resistance to eddy currents, thereby minimizing energy loss due to circulating currents induced in the core.

The emf (E) induced in a self-inductance L is given by E = L * (dI/dt). Here, dI = 2 A - 3 A = -1 A, dt = 1 ms = 0.001 s, so dI/dt = -1000 A/s. Taking magnitude, L = E / |dI/dt| = 5 V / 1000 A/s = 0.005 H = 5 mH.

The surface charge density (σ) is calculated by dividing the total charge (q) by the total surface area (A) of the cube. For a cube with side length 5 cm (0.05 m), the surface area is 6 × (0.05 m)² = 6 × 0.0025 m² = 0.015 m². Given the charge q = 6 C, the surface charge density is σ = q / A = 6 C / 0.015 m² = 400 C/m². This matches option D, not option A. Therefore, the correct answer is D.

A current of one microampere (1 μA = 1×10⁻⁶ A) corresponds to a charge flow of 1×10⁻⁶ coulombs per second. Since one electron carries a charge of approximately 1.6×10⁻¹⁹ coulombs, the number of electrons per second is (1×10⁻⁶ C/s) ÷ (1.6×10⁻¹⁹ C/electron) ≈ 6.25×10¹² electrons per second.

The farad is the SI unit of capacitance, which measures a capacitor's ability to store charge per unit voltage. It is named after Michael Faraday.

Ohm is the SI unit of electrical resistance, which measures how much a material opposes the flow of electric current.

Kirchhoff's 2nd rule, also known as the loop rule or Kirchhoff's voltage law, states that the algebraic sum of all potential differences (voltage drops) around any closed loop in a circuit is zero. This means that the sum of the electromotive forces (emfs, such as battery voltages) in the loop is equal to the sum of the IR drops (voltage drops across resistors) in that loop. Therefore, Kirchhoff's 2nd rule involves both IR drops and battery emf, not just IR drops alone.

Copper is a metal, and its resistance decreases as temperature decreases because electron scattering reduces. Germanium is a semiconductor, and its resistance increases as temperature decreases because fewer charge carriers are thermally excited at lower temperatures.

Two parallel beams of positrons, which are positively charged particles, will repel each other due to the electrostatic repulsion between like charges. This is consistent with Coulomb's law, where like charges repel.

When a second electron is brought closer to the first electron, both being negatively charged, the electrostatic potential energy increases due to the repulsive force between like charges. This increase reflects the work done against the repulsion to bring them closer.

When a motor is just started, its rotor speed is zero, so the back emf, which depends on the rotor speed, is also zero. As the motor speeds up, the back emf increases.

Tesla (T) is the SI unit of magnetic flux density or magnetic induction, which measures the strength of a magnetic field. It is not used for magnetic intensity or magnetic moment.

The Coulomb force between two charges in a medium is reduced by the medium's relative permittivity (dielectric constant). For water at room temperature, the dielectric constant is approximately 78 to 80, meaning the Coulomb force is reduced to about 1/78 or 1/80 of its value in vacuum. This is a well-established physical fact. The option '1/78 times' (option C) correctly reflects this reduction factor. The option '1/58 times' (option D) is not accurate for water's dielectric constant at standard conditions. Therefore, the correct answer is C.

Both alternating current (A.C.) and direct current (D.C.) produce the same heating effect when passing through a resistance, as the heating depends on the power dissipated (I²R), which is similar for equal RMS currents.

An electric motor can be used as a dynamo (generator) because both devices operate on the principle of electromagnetic induction; when an electric motor is driven mechanically, it generates electricity, functioning as a dynamo.

Conductance (G) is the reciprocal of resistance (R). Given R = 0.5 ohm, G = 1 / 0.5 = 2 siemens (S).

The field particle of electromagnetic interaction is the photon, which is the quantum of the electromagnetic field and mediates electromagnetic forces.

A shunt is a low resistance path that allows current to bypass a part of a circuit, commonly used to divert current around a component.

The visible spectrum of light ranges approximately from 3900 to 7600 angstroms, which corresponds to wavelengths visible to the human eye. This range covers violet to red light.

1 Weber per square meter (Wb/m²) is the SI unit of magnetic flux density equivalent to 1 Tesla. Since 1 Tesla equals 10,000 Gauss, 1 Wb/m² equals 10,000 Gauss. Therefore, the correct answer is option C: 10⁴ gauss.

Ceramic magnets, also known as ferrite magnets, are made from ceramic materials which are electrical insulators. They do not conduct electricity, hence they are classified as insulators.

The drift velocity of free electrons in a wire is directly proportional to the applied potential difference (voltage). Therefore, if the potential difference is doubled, the drift velocity will also double.