Fields — Free Physics HL Practice Questions

A remote mining facility in northern Canada is powered by a $50\,\text{Hz}$ AC generator that produces $12\,\text{kV}$ at the output terminals. The facility is connected to a transformer substation $85\,\text{km}$ away via a pair of copper transmission cables, each with a resistance of $0.015\,\Omega\,\text{km}^{-1}$. The substation contains a step-down transformer that reduces the voltage to $240\,\text{V}$ for local use. The total power demand of the facility is $5.4\,\text{MW}$ at a power factor of $0.95$ (lagging). Assume ideal transformer operation and that the transmission line operates at the generator voltage.

A remote mining facility in northern Canada receives electrical power from a hydroelectric plant $250\,\text{km}$ away. The plant generates $5.0\,\text{MW}$ at $25\,\text{kV}$ and uses a step-up transformer to raise the transmission voltage to $500\,\text{kV}$. The transmission line has a total resistance of $12\,\Omega$. The facility requires the power at $480\,\text{V}$.

A large-scale magnetic braking system for a roller coaster uses a rectangular copper plate of length $L = 1.2 \text{ m}$ and width $w = 0.60 \text{ m}$, moving horizontally through a uniform magnetic field of magnitude $B = 0.40 \text{ T}$. The field is confined to a region of length $d = 0.30 \text{ m}$ in the direction of motion. The plate moves with constant velocity $v = 15 \text{ m s}^{-1}$ perpendicular to the field. The plate has thickness $t = 5.0 \text{ mm}$ and resistivity $\rho = 1.7 \times 10^{-8} \ \Omega \text{ m}$. The magnetic field is perpendicular to the plane of the plate.

A hospital uses a step-down transformer to reduce the mains voltage from $240\,\text{V}$ to $12\,\text{V}$ for powering medical imaging equipment. The primary coil has $2000$ turns. The secondary coil supplies a current of $8.0\,\text{A}$ to the imaging equipment.

A research facility uses a velocity selector to filter charged particles. A beam of alpha particles ($\text{He}^{2+}$) enters a region where a uniform magnetic field of $0.20\,\text{T}$ acts perpendicular to the beam, and a uniform electric field acts perpendicular to both the beam and the magnetic field. The alpha particles travel straight through without deflection at a speed of $5.0 \times 10^{5}\,\text{m s}^{-1}$. $$\text{Charge of alpha particle} = 3.20 \times 10^{-19}\,\text{C}$$ $$\text{Mass of alpha particle} = 6.64 \times 10^{-27}\,\text{kg}$$ -

In a nuclear fusion reactor, a beam of deuterium ions ($^2\text{H}^+$) is injected into a magnetic confinement field. Each ion has a speed of $1.2 \times 10^6\,\text{m s}^{-1}$ and moves perpendicular to a uniform magnetic field of strength $0.65\,\text{T}$.

Magnesium ions, each with charge $+1.60 \times 10^{-19}\,\text{C}$, are accelerated from rest through a potential difference of $2500\,\text{V}$. They then enter a uniform magnetic field of strength $0.32\,\text{T}$, directed perpendicular to their velocity. The ions follow semicircular paths and strike a detector. $$\text{Mass of }^{24}\text{Mg ion} = 3.98 \times 10^{-26}\,\text{kg} \qquad \text{Mass of }^{26}\text{Mg ion} = 4.32 \times 10^{-26}\,\text{kg}$$

A research team uses a velocity selector to filter charged particles from a nuclear reactor sample. The velocity selector consists of perpendicular uniform electric and magnetic fields. The electric field is produced by parallel plates $0.050\,\text{m}$ apart with a potential difference of $200\,\text{V}$. The magnetic field strength in the selector is $0.040\,\text{T}$. After passing through the selector, particles enter a region containing only a uniform magnetic field of strength $0.040\,\text{T}$, directed identically to the field in the selector, where they follow circular paths. For a particular particle: - charge $q = 3.20 \times 10^{-19}\,\text{C}$ - mass $m = 6.64 \times 10^{-27}\,\text{kg}$

A point charge of $+4.0 \times 10^{-9}\,\text{C}$ is placed at the origin of a coordinate system. A second point charge of $-2.0 \times 10^{-9}\,\text{C}$ is placed on the x-axis at $x = 0.30\,\text{m}$. Point P is on the x-axis at $x = 0.10\,\text{m}$. Coulomb constant: $k = 8.99 \times 10^{9}\,\text{N\,m}^{2}\,\text{C}^{-2}$

An industrial electrostatic precipitator uses a charged wire to remove dust particles from exhaust gases. The wire is at a potential of $-5000\,\text{V}$ relative to a grounded collecting plate $0.050\,\text{m}$ away. The electric field between the wire and plate is approximately uniform.

A diagnostic system in a nuclear fusion reactor prototype uses a charged particle detector. A spherical electrode of radius $r_0 = 0.050\,\text{m}$ is charged to a potential of $V_0 = +5000\,\text{V}$ relative to ground. A dust particle of mass $m = 2.5 \times 10^{-12}\,\text{kg}$ and charge $q = +3.2 \times 10^{-15}\,\text{C}$ is released from rest a distance $r_i = 0.80\,\text{m}$ from the centre of the electrode. The particle moves radially toward the electrode under the influence of the electric field only. The electrode may be treated as a point charge located at its centre for all positions outside its surface.

Two horizontal parallel plates are separated by $0.040\,\text{m}$. The upper plate is at a potential of $+200\,\text{V}$ and the lower plate is at $0\,\text{V}$. A charged oil drop of mass $3.2 \times 10^{-15}\,\text{kg}$ is held stationary between the plates. Gravitational field strength $g = 9.81\,\text{m s}^{-2}$

A team of planetary scientists analyses data from a probe in a circular polar orbit an altitude of $240\,\text{km}$ above the surface of Xylos, a planet with no atmosphere. The surface gravitational field strength of Xylos is $g_s = 8.4\,\text{N\,kg}^{-1}$ and its radius is $R = 3.20 \times 10^{6}\,\text{m}$. The mass of the probe is $m = 500\,\text{kg}$.

The exoplanet Kepler-452b orbits host star in an elliptical orbit. At its closest approach (periastron), the planet is $r_p = 1.04 \times 10^{11}\,\text{m}$ from the star and moves with speed $v_p = 2.85 \times 10^4\,\text{m s}^{-1}$. At its farthest point (apastron), the distance is $r_a = 1.56 \times 10^{11}\,\text{m}$.

A binary star system consists of two stars, Aldebor and Bellatrix, orbiting their common centre of mass. The orbital radius of Aldebor is $r_A = 4.0 \times 10^{9}\,\text{m}$ and the orbital period of the system is $T = 2.5\,\text{years}$. The mass of Aldebor is $M_A = 2.0 \times 10^{30}\,\text{kg}$. Assume circular orbits. $1\,\text{year} = 3.15 \times 10^{7}\,\text{s}$, $G = 6.67 \times 10^{-11}\,\text{N\,m}^2\,\text{kg}^{-2}$.

The dwarf planet Ceres orbits the Sun in an elliptical orbit with a semi-major axis of $2.77\,\text{AU}$. The orbital period of Ceres is $4.60\,\text{years}$. The dwarf planet Haumea has an orbital period of $283\,\text{years}$.

A rural community is supplied with electrical power from a distant hydroelectric plant via a long-distance transmission line. The plant generates power at $25\,\text{kV}$ rms. A step-up transformer at the plant increases this to $400\,\text{kV}$ rms for transmission. The transmission line has a total resistance of $12.0\,\Omega$. A step-down transformer at the community substation reduces the voltage to $11\,\text{kV}$ rms for local distribution. Both transformers are ideal. The community draws $5.0\,\text{MW}$ of average power.

A medical linear accelerator (linac) uses a step-up transformer to power its electron gun. The primary coil has $N_p = 200$ turns and is connected to a $230\,\text{V}_{\text{rms}}$, $50\,\text{Hz}$ mains supply. The secondary coil supplies $25\,\text{kV}_{\text{rms}}$ to the electron gun. The transformer core has a cross-sectional area of $0.040\,\text{m}^2$.