Name: current density in wires and solutions
Uploaded: 2023-04-30T12:38:44.000Z
Duration: 1 min 21 s
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Physical Science

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PS.PSc.6.2

Current Density

Current density is the total amount of current flowing per unit cross-sectional area, measured in amperes per square meter.
When a small current flows through an infinitesimal area, a relationship between the current and the current density can be established, where theta is the angle between the area and the current density. Therefore, the total current passing through the area can be determined by integrating it over the area.
Consider the magnitude of the current density and recall the equation of drift velocity. By substituting the terms, a relation between current density and drift velocity can be established. While current is a scalar quantity, current density is a vector quantity.
Consider a current of 0.5 amperes flowing through a 50-watt bulb. The bulb is wired using a copper wire with a radius of 1.25 mm. Determine the magnitude of the current density.
The known values are the current and cross-sectional area, whereas the current density is an unknown quantity. By substituting the known quantities into the equation, the current density can be determined.

current density

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, the amount of current flowing through a conductor is the same at all points along the conductor, even if the conductor area varies. The current density consists of the local magnitude and direction of the charge flow, which varies from point to point. Current density is measured in amperes per meter square, and direction is defined as the net flow of positive charges through the area. Also, for any given current, as the diameter of the wire in a circuit increases, the charge density decreases. The magnitude of the current density is the current divided by the area.
<img alt="Current density equation J=I/A; static formula; vital in electromagnetism studies." src="/files/ftp_upload/13745/13745_Equation_1.svg" style="text-align: center; height: 28px;" data-altupdatedat="1761830439000" data-alt="Equation1" />
<img alt="Current density equation \( J = n|q|v_d \), formula in physics, charge transport concept." src="/files/ftp_upload/13745/13745_Equation_2v2.svg" style="text-align: center; height: 14px;" data-altupdatedat="1761830439000" data-alt="Equation2" />
Thus, the current density can be determined as:
<img alt="Electric current density equation \( \mathbf{J} = nq\mathbf{v}_d \); vector notation in physics." src="/files/ftp_upload/13745/13745_Equation_3v2.svg" style="text-align: center; height: 22px;" data-altupdatedat="1761830439000" data-alt="Equation3" />
If q is positive, drift velocity is in the same direction as the electrical field. If q is negative, drift velocity is in the opposite direction to the electric field. Either way, the direction of the current density is in the direction of the electrical field. For example, in a sodium chloride solution, current can be carried by both positive sodium ions and negative chlorine ions; the total current is found by adding up the currents due to each kind of charged particle.

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, ...

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Current and Resistance

KEY TERMS AND CONCEPTS

current density in wires and solutions

Current density describes how much electric current passes through a given cross-sectional area. It helps show not just the size of the current, but also how it is distributed through a conductor. The current density can change from point to point because the local charge flow can vary.

If the current flow is uniform, the amount of current is the same at every point along the conductor, even when the conductor’s area changes. Current density is measured in amperes per square meter. Its direction is defined by the net flow of positive charges through the area.

For a given current, a larger wire diameter means a lower charge density. The magnitude of current density is found by dividing current by area. The direction of current density matches the direction of the electric field.

The drift velocity of charged particles depends on charge sign. If q is positive, the drift velocity is in the same direction as the electric field. If q is negative, the drift velocity is opposite to the electric field. In sodium chloride solution, both sodium ions and chlorine ions can carry current, so the total current is the sum of the current from each type of charged particle.

Current Density in Wires and Solutions

electrical current

Current Flow in Simple Circuits

Electrical current is the flow of charge in a circuit. A large current means a large amount of charge moves through a wire in a short time. A small current means only a small amount of charge moves through the circuit over a longer time. Examples include the current needed to run a refrigerator and the smaller current used by a handheld calculator. The SI unit for current is the ampere, or amp. It is named for the French physicist André-Marie Ampère (1775–1836). One ampere means one coulomb of...

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Current density describes how much electric current passes through a given cross-sectional area. It helps show not just the size of the current, but also how it is distributed through a conductor. The current density can change from point to point because the local charge flow can vary. If the current flow is uniform, the amount of current is the same at every point along the conductor, even when the conductor’s area changes. Current density is measured in amperes per square meter. Its...

resistivity

Resistivity in Conductors and Insulators

Resistivity describes how much a material opposes electric current. When a voltage is applied to a conductor, an electric field forms. The charges in the conductor feel that force, and a current density develops. In some materials, including metals at a given temperature, the current density is approximately proportional to the electric field. In those cases, current density can be modeled with conductivity, written as sigma. Electrical conductivity is measured in (ohm·m)^−1. It tells how well...

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Cutting Electric Bills with Efficient Lighting

Electrical energy is the energy transferred when electrons move from one point to another. The longer an appliance is used, the more electrical energy it consumes. If power stays constant, electrical energy equals the power used by the device times the time it runs. That is why longer use leads to a higher electric bill. Electric bills measure this energy in kilowatt-hours. One kilowatt-hour is equal to 3.6 × 10^6 joules. You can lower electrical energy use by cutting the time an appliance...

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Resistance and Ohm's law help explain how electric current moves through a conductor. In a perfect conductor, the electric field inside is zero because free electrons move to cancel it. Any extra charge then stays on the surface. In a practical conductor, an applied electric field can remain in place. That field drives electrons through the material and creates a current. The current density, which is current per unit area, is related to the electric field. More generally, it is related to the...

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Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction. In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions...

key terms and concepts

Explore current density in wires and sodium chloride solution. Learn how current, area, charge sign, and electric field determine its direction and size.

Current Density in Wires and Solutions | JoVE K12

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Current Density in Wires and Solutions

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