Fields — Free Physics SL Practice Questions

A spherical asteroid of radius $R = 3.2 \times 10^3\,\text{m}$ has uniform density $\rho = 2.7 \times 10^3\,\text{kg m}^{-3}$. A small probe of mass $m = 1.2 \times 10^3\,\text{kg}$ is placed at point $P$, a distance $d = 1.5R$ from the centre of the asteroid. $G = 6.67 \times 10^{-11}\,\text{N m}^2\,\text{kg}^{-2}$

A comet orbits the Sun in an elliptical orbit. At its closest approach (perihelion), the comet is $8.0 \times 10^{10}\,\text{m}$ from the Sun and has a speed of $5.4 \times 10^4\,\text{m s}^{-1}$. At its farthest point (aphelion), the comet is $3.2 \times 10^{11}\,\text{m}$ from the Sun.

A binary star system consists of two stars, Star X and Star Y, in circular orbits about their common centre of mass. The mass of Star X is $M_X = 4.0 \times 10^{30}\,\text{kg}$ and the mass of Star Y is $M_Y = 2.0 \times 10^{30}\,\text{kg}$. The separation between their centres is $d = 8.0 \times 10^{10}\,\text{m}$. $$G = 6.67 \times 10^{-11}\,\text{N\,m}^2\,\text{kg}^{-2}$$

A deep-space probe is approaching a planet of mass $M = 6.0 \times 10^{24}\,\text{kg}$ and radius $R = 6.4 \times 10^6\,\text{m}$. At a certain instant, the probe is at a distance $r = 2.0 \times 10^7\,\text{m}$ from the planet's centre and has a speed $v = 4.0 \times 10^3\,\text{m s}^{-1}$ directed radially away from the planet. The probe's mass is $m = 1.5 \times 10^3\,\text{kg}$. $G = 6.67 \times 10^{-11}\,\text{N m}^2\,\text{kg}^{-2}$

A satellite is placed in an elliptical orbit around Earth. The satellite's distance from Earth's centre varies between $r_p = 7.0 \times 10^6\,\text{m}$ at perigee (closest point) and $r_a = 1.4 \times 10^7\,\text{m}$ at apogee (farthest point). The speed of the satellite at perigee is $v_p = 8.5 \times 10^3\,\text{m s}^{-1}$.

A simple electric motor in a power tool consists of a rectangular coil of wire with $50$ turns, each of area $8.0 \times 10^{-4}\,\text{m}^2$, placed in a uniform magnetic field of strength $0.40\,\text{T}$. The coil rotates about an axis perpendicular to the field. The motor is connected to a battery of emf $12\,\text{V}$, and the coil has a total resistance of $2.0\,\Omega$.

A loudspeaker uses an electromagnet to produce sound. A coil of $80$ turns is placed in a radial magnetic field of strength $0.15\,\text{T}$. The length of wire in the magnetic field per turn is $0.040\,\text{m}$. A current of $0.50\,\text{A}$ flows through the coil, exerting a force on the coil and moving the speaker cone.

A medical linear accelerator uses a high-voltage electrostatic system to accelerate electrons for cancer treatment. Electrons are injected with negligible initial speed into a uniform electric field between two parallel conducting plates separated by $d = 0.120\,\text{m}$. The plates are connected to a potential difference of $\Delta V = 2.0 \times 10^{6}\,\text{V}$. The electrons travel from the negative plate to the positive plate. $$q_e = 1.60 \times 10^{-19}\,\text{C}, \quad m_e = 9.11 \times 10^{-31}\,\text{kg}, \quad c = 3.00 \times 10^{8}\,\text{m s}^{-1}$$

A solenoid used in an MRI machine has $N = 500$ turns and a length of $L = 0.40\,\text{m}$. It carries a current of $I = 2.0\,\text{A}$. Permeability of free space: $\mu_0 = 4\pi \times 10^{-7}\,\text{T\,m\,A}^{-1}$ -

A medical linear accelerator (linac) uses a series of charged plates to accelerate electrons for cancer treatment. Consider a simplified model where an electron is initially at rest at the negative plate of a parallel-plate arrangement. The plates are separated by a distance of $0.12\,\text{m}$ and the uniform electric field between them has a magnitude of $2.5 \times 10^{4}\,\text{N C}^{-1}$, directed from the positive plate toward the negative plate.

A rectangular current-carrying loop is placed in a uniform magnetic field directed into the page. The loop has width $w = 0.12\,\text{m}$ and height $h = 0.080\,\text{m}$, carries a current $I = 5.0\,\text{A}$ clockwise, and the magnetic field has magnitude $B = 0.40\,\text{T}$. The loop is free to rotate about a vertical axis through its centre. The plane of the loop is initially perpendicular to the magnetic field. - $F = BIL\sin\theta$ - $\tau = BIAN\sin\phi$, where $\phi$ is the angle between the plane of the loop and the field direction

A medical cyclotron accelerates protons for cancer treatment. The magnetic field strength is $0.85\,\text{T}$. A proton enters the magnetic field with a velocity of $3.2 \times 10^{6}\,\text{m s}^{-1}$ perpendicular to the field lines. $$q = 1.60 \times 10^{-19}\,\text{C} \qquad m_p = 1.67 \times 10^{-27}\,\text{kg}$$

A proton beam is used in a medical cyclotron for cancer therapy. Protons are injected with negligible initial speed and accelerated by an alternating electric field between two D-shaped electrodes (dees). A uniform magnetic field of strength $B = 0.85\,\text{T}$ causes the protons to follow semicircular paths of increasing radius. The maximum radius before extraction is $r = 0.45\,\text{m}$. Proton

A beam of singly charged lithium ions ($\text{Li}^+$) enters a region of uniform magnetic field of strength $B = 0.45\,\text{T}$, directed into the page. The ions travel horizontally to the right with speed $v = 4.0 \times 10^5\,\text{m s}^{-1}$, perpendicular to the field. The ions follow a circular arc of radius $r = 0.026\,\text{m}$. $$q = 1.60 \times 10^{-19}\,\text{C}$$

An electron beam in a cathode ray tube is directed into a uniform magnetic field of strength $0.030\,\text{T}$. The electrons have a kinetic energy of $2.0 \times 10^{-16}\,\text{J}$ and enter the field at right angles. $$m_e = 9.11 \times 10^{-31}\,\text{kg}, \quad |q_e| = 1.60 \times 10^{-19}\,\text{C}$$