Laplace Force and Electromagnetic Induction

Comprehensive vocabulary flashcards covering Laplace Force, magnetic flux, Lenz's Law, and electromagnetic induction principles based on the lecture transcript.

Laplace Force

The force applied to the middle of a rectilinear portion of a conductor of length $l$ placed in a magnetic field $\mathbf{B}$ and traversed by a current $I$.

Magnitude of Laplace Force

$F = I l B |\sin(\alpha)|$ where $\alpha = (\mathbf{l}, \mathbf{B})$.

Direction of Laplace Force

The force is perpendicular to the plane formed by the conductor length $\mathbf{l}$ and the magnetic field vector $\mathbf{B}$, noted as $\mathbf{F} \perp (l, B)$.

Right-hand rule (Laplace Force)

The method used to determine the sense (direction) of the Laplace force.

Laplace equilibrium with vertical $\mathbf{B}$

The state where $\sum \mathbf{F} = 0$ leading to the relation $IB = mg \tan(\alpha)$, or $F = mg \tan(\alpha)$, when the magnetic field remains vertical on an inclined plane.

Normal to the surface ($\mathbf{n}$)

A vector originating at the center of surface $S$, perpendicular to the surface, with a magnitude of $||\mathbf{n}|| = 1$, and a sense determined by the right-hand rule based on the chosen positive orientation of the contour.

Magnetic Flux ($\Phi$)

The quantity of magnetic field lines $\mathbf{B}$ passing through a surface $S$, expressed as $\Phi = \mathbf{B} \cdot \mathbf{S} = BS \cos(\theta)$ where $\theta = (\mathbf{B}, \mathbf{n})$.

Weber [Wb]

The unit of measurement for magnetic flux.

Magnetic flux in a solenoid

The flux through a solenoid with $N$ turns, given by $\Phi = NBS \cos(\theta)$.

Electromagnetic Induction Phenomenon

The appearance of an induced electromotive force $e$ due to the variation of magnetic flux $\Phi$.

Average induced electromotive force ($e$)

$$e = -\frac{\Delta \Phi}{\Delta t} = -\frac{\Phi_2 - \Phi_1}{\Delta t}$$

Instantaneous induced electromotive force ($e$)

The value of the induced force at a specific moment, given by $e = -\frac{d\Phi}{dt}$.

Lenz's Law

The principle represented by the negative sign in the EMF expression, stating that the sense of the induced current opposes the cause that produced it.

Induced current ($i$)

The current in a closed circuit given by $i = \frac{e}{\sum R}$, where $\sum R$ is the total resistance.

Induced quantity of electricity ($Q$)

The average quantity of electricity circulating during a flux variation $\Delta \Phi$, calculated as $Q = \frac{|\Delta \Phi|}{\sum R}$.

Magnetic field $\mathbf{B}$ in a solenoid

The field produced by a solenoid with $N$ turns and length $l$ carrying current $i$, expressed as $B = \frac{\mu_0 N i}{l}$.

Induced EMF for a rotating circuit

The force produced when $\theta = \omega t$, resulting in $\Phi = NBS \cos(\omega t)$ and $e = \omega NBS \sin(\omega t)$, where $e_{max} = \omega NBS$.

Lenz's Law condition for opposite $\mathbf{B}$ and $\mathbf{B'}$

If the magnetic flux $\Phi$ is increasing ($\Delta \Phi > 0$), then the inductor field $\mathbf{B}$ and the induced field $\mathbf{B'}$ have opposite senses.

Lenz's Law condition for same sense $\mathbf{B}$ and $\mathbf{B'}$

If the magnetic flux $\Phi$ is decreasing ($\Delta \Phi < 0$), then the inductor field $\mathbf{B}$ and the induced field $\mathbf{B'}$ have the same sense.