During thunderstorms or near high-voltage equipment, engineers rely on the principle of electrostatic shielding. A Faraday cage is an enclosure made of conducting material (like a metal mesh). Because charges in a conductor are free to move, any external electric field causes the charges to instantly rearrange themselves until the net electric field inside the conductor is exactly zero. This is why you are safe inside a metal car during a lightning strike; the electricity travels through the skin of the car and into the ground, leaving the interior completely shielded from the deadly electric fields.

A DC electric motor is a direct application of the Lorentz force law. It consists of a loop of wire (the armature) carrying a current, placed inside a strong, permanent magnetic field. According to $\vec{F} = I(\vec{L} \times \vec{B})$, the magnetic field exerts a force on the moving electrons in the wire. Because the current travels in opposite directions on opposite sides of the loop, one side is pushed up while the other is pushed down, creating a torque ($\tau$) that spins the motor. A commutator reverses the current direction every half-turn to keep the torque pushing in the same rotational direction, converting electrical energy into continuous mechanical rotation.

Two point charges, $q_1 = +3.0 \mu\text{C}$ and $q_2 = -5.0 \mu\text{C}$, are separated by a distance of $0.2 \text{ m}$ in a vacuum. What is the magnitude of the electrostatic force between them? ($k = 8.99 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2$)

A point charge $q = -4.0 \text{ nC}$ is located at the origin. What is the magnitude and direction of the electric field at a point $P$ located $0.5 \text{ m}$ away on the positive x-axis?

Two point charges are located on the y-axis: $q_1 = +2.0 \mu\text{C}$ at $y = 0.3 \text{ m}$, and $q_2 = +2.0 \mu\text{C}$ at $y = -0.3 \text{ m}$. Find the net electric field at point $P$ on the x-axis at $x = 0.4 \text{ m}$.

A $12 \text{ V}$ car battery is connected across a single headlight bulb. A current of $3.0 \text{ A}$ flows through the circuit. What is the resistance of the bulb, and how much power does it dissipate?

A $9 \text{ V}$ battery is connected to a circuit containing three resistors. Resistor $R_1$ ($10 \ \Omega$) is in series with a parallel combination of $R_2$ ($20 \ \Omega$) and $R_3$ ($30 \ \Omega$). What is the total equivalent resistance of the circuit?

Using the circuit from the previous example ($9 \text{ V}$ battery, total $R_{eq} = 22 \ \Omega$), what is the current flowing out of the battery, and what is the voltage drop across $R_1$ ($10 \ \Omega$)?

An electron ($q = -1.6 \times 10^{-19} \text{ C}$) is moving at $5.0 \times 10^6 \text{ m/s}$ due East through a uniform magnetic field of $2.0 \text{ T}$ pointing due North. What is the magnitude and direction of the magnetic force on the electron?

A straight segment of wire $0.5 \text{ m}$ long carries a current of $4.0 \text{ A}$. It is placed in a uniform magnetic field of $0.8 \text{ T}$. If the wire experiences a maximum magnetic force of $1.6 \text{ N}$, what must be the angle between the wire and the magnetic field?

Two long, straight, parallel wires are separated by $0.1 \text{ m}$. Wire A carries a current of $5.0 \text{ A}$ upwards. Wire B carries a current of $8.0 \text{ A}$ downwards. What is the magnitude and direction of the net magnetic field halfway between the two wires? ($\mu_0 = 4\pi \times 10^{-7} \text{ T}\cdot\text{m/A}$)