Moving Charges and Magnetism

Practice vocabulary flashcards based on the fundamental concepts of electromagnetism, Lorentz force, Biot-Savart law, and galvanometers from chapter four.

Hans Christian Oersted

Danish physicist who discovered in 1820 that an electric current in a straight wire caused a deflection in a nearby magnetic compass needle.

Lorentz Force

The total force acting on a point charge $q$ moving with velocity $\mathbf{v}$ in the presence of both electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$, expressed as $\mathbf{F} = q [ \mathbf{E}(\mathbf{r}) + \mathbf{v} \times \mathbf{B}(\mathbf{r}) ]$.

Tesla ($T$)

The SI unit of magnetic field; the magnitude is $1$ unit when the force on a charge of $1\,C$ moving perpendicular to the field at $1\,m/s$ is $1\,N$.

Gauss ($G$)

A non-SI unit used to measure magnetic field, where $1\,G = 10^{-4}\,tesla$.

Cyclotron Frequency ($\nu_c$)

The frequency of uniform circular motion for a charge in a plane normal to a magnetic field, given by the formula $\nu_c = \frac{qB}{2\pi m}$.

Pitch ($p$)

The distance moved by a charged particle along the magnetic field during one rotation in helical motion, given by $p = v_{\parallel} T = \frac{2\pi m v_{\parallel}}{qB}$.

Biot-Savart Law

A vector relationship defining the magnetic field $d\mathbf{B}$ produced by an infinitesimal current element $I d\mathbf{l}$ at distance $r$, given by $d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}$.

Permeability of free space ($\mu_0$)

The proportionality constant in the Biot-Savart law with an exact value of $4\pi \times 10^{-7}\,T\,m/A$.

Ampere's Circuital Law

States that the line integral of the magnetic field $\mathbf{B}$ over a closed loop is equal to $\mu_0$ times the total current $I$ passing through the surface: $\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I$.

Amperian Loop

A closed loop chosen such that at each point, the magnetic field is either tangential with constant magnitude, normal to the loop, or vanishes, facilitating the evaluation of magnetic fields.

Solenoid

A device consisting of a long wire wound in the form of a helix with closely spaced turns; the internal magnetic field is uniform and given by $B = \mu_0 n I$.

Ampere ($A$)

The value of a steady current which, when maintained in each of two very long, straight, parallel conductors placed $1\,m$ apart in vacuum, produces a force of $2 \times 10^{-7}\,newtons$ per metre of length.

Magnetic Moment ($\mathbf{m}$)

A vector quantity for a current loop of area $\mathbf{A}$ with $N$ turns carrying current $I$, defined as $\mathbf{m} = N I \mathbf{A}$.

Moving Coil Galvanometer (MCG)

An instrument consisting of a coil free to rotate in a uniform radial magnetic field; the steady angular deflection $\phi$ is proportional to the current $I$.

Current Sensitivity

The deflection per unit current in a galvanometer, expressed by the constant $\frac{NAB}{k}$, where $k$ is the torsional constant of the spring.

Voltage Sensitivity

The deflection per unit voltage in a galvanometer, given by $\frac{\phi}{V} = \frac{NAB}{kR}$.

Shunt Resistance ($r_s$)

A small resistance connected in parallel with a galvanometer coil to convert it into an ammeter for measuring higher currents.

Torque (on a current loop)

The rotational force experienced by a loop of magnetic moment $\mathbf{m}$ in a uniform magnetic field $\mathbf{B}$, given by $\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}$.