Category: Part 3: Electricity

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Irodov Problem 3.21 (Section 3.1: Constant Electric Field in Vacuum): This problem applies the fundamental laws of electrostatics to a specific charge configuration involving potential energy of point charge system. Charge parameters and geometry as specified in Irodov Given Information Mass $m$, velocity $v$, height…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.355 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Show that the force on dipole $\vec{p}$ in non-uniform field $\vec{E}$ is $\vec{F} = \nabla(\vec{p}\cdot\vec{E})$. Calculate for $\vec{p} = p\hat{x}$ with field varying along $x$. $\vec{p} = p\hat{x}$, $E = E(x)$ In non-uniform fields, forces on $+q$ and Given…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.356 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.353 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…

Problem Statement Solve the rotational mechanics problem: Solve the work-energy problem: Find the torque on a dipole $\vec{p}$ in uniform field $\vec{E}$, the potential energy, and equilibrium stability. $\vec{p}$ = dipole moment, $\vec{E}$ = uniform field, $\theta$ = angle between them Net force is zero (uniform field). Torque aligns the dipole with the f Given…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.354 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…

Problem Statement Solve the magnetic field/force problem: Problem 3.351 — Magnetic fields and forces $c = 3\times10^8\,\text{m/s}$ Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each body is treated separately wi Given Information Current $I$ or charge $q$…

Problem Statement An electric dipole of moment $p = ql$ is at the origin. Find the potential $\varphi$ and field $E$ at distance $r \gg l$ at angle $\theta$ from the dipole axis. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.352 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…