Understanding Current Density and Electromotive Force

Classified in Physics

Written at November 19, 2024 on English with a size of 2.16 KB.

Current Density

The electric current density is a vector quantity representing power per unit area. It relates to current as:

$I = \int_S \mathbf{j} \cdot d \mathbf{S}$

I is the electric current in amperes (A).
j is the current density in amperes per square meter (Am^-2).
S is the area in square meters (m²).

Isolated Point Charges

Current density relates to charge carriers (electrons, holes, ions) by:

$\mathbf{j} = \sum_i n_i q_i \mathbf{v}_i$

Where:

n_i is the concentration of carrier i.
q_i is the electric charge of carrier i.
v_i is the average velocity of carrier i in the volume.

Electromotive Force (EMF)

Electromotive force maintains a potential difference in an open circuit or produces current in a closed circuit. It's a generator characteristic, explained by an electric field Ξ, where $\int_S \xi ds$ defines the EMF.

EMF is the work done to move a unit positive charge from negative to positive inside the generator, measured in volts (V).

$P = \frac{R}{A}$

It relates to potential difference V and internal resistance r by: E = V + Ir. (Ir is the potential drop inside the generator due to resistance).

The induced EMF in a closed circuit equals the rate of change of magnetic flux Φ: $\Xi = - \frac{\Delta \Phi}{\Delta t}$ (Faraday's Law). The negative sign (Lenz's Law) indicates the induced EMF opposes the flux change.

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