Two long, parallel wires are separated by a dis- Figure...

Two long, parallel wires are separated by a dis- Figure E28.29 tance of $0.400 \mathrm{~m}$ (Fig. E28.29). s* The currents $I_{1}$ and $I_{2}$ have the directions shown. (a) Calculate the magnitude of the force $\mathrm{ex}-$ erted by each wire on a $1.20 \mathrm{~m}$ length of the other. Is the force attractive or repulsive? (b) Each current is doubled, so that $I_{1}$ becomes $10.0 \mathrm{~A}$ and $I_{2}$ becomes $4.00 \mathrm{~A}$. Now what is the magnitude of the force that each wire exerts on a $1.20 \mathrm{~m}$ length of the other?

Two long, parallel wires are separated by a dis- Figure E28.29 tance of $0.400 \mathrm{~m}$ (Fig. E28.29). s*
The currents $I_{1}$ and $I_{2}$ have the directions shown. (a) Calculate the magnitude of the force $\mathrm{ex}-$ erted by each wire on a $1.20 \mathrm{~m}$ length of the other. Is the force attractive or repulsive? (b) Each current is doubled, so that $I_{1}$ becomes $10.0 \mathrm{~A}$ and $I_{2}$ becomes $4.00 \mathrm{~A}$. Now what is the magnitude of the force that each wire exerts on a $1.20 \mathrm{~m}$ length of the other?

Key Concepts

Effect of Current Magnitude on Magnetic Interaction

The strength of the magnetic field and the resulting force between current-carrying wires are proportional to the current magnitude. Doubling the current in each wire leads to a corresponding increase in the magnetic field strength and the force experienced by the wires. This concept is critical for understanding how variations in current affect the force between parallel conductors.

Interaction Between Parallel Currents

Two parallel wires carrying electric currents interact magnetically; the force between them depends on the direction of the currents. If the currents flow in the same direction, the wires attract each other, whereas if they flow in opposite directions, the wires repel each other. This principle is a direct consequence of the magnetic field each wire produces and how these fields interact with the other wire.

Magnetic Field Produced by a Current-Carrying Wire

A current-carrying wire generates a magnetic field that surrounds it. The field's magnitude at a given distance from the wire is determined by Ampère's law, which shows that the field strength is directly proportional to the current and inversely proportional to the distance from the wire. This concept serves as the basis for calculating magnetic fields in scenarios with long, straight conductors.

Magnetic Force on a Current-Carrying Conductor

A conductor carrying a current experiences a force when it is placed in a magnetic field. This force is given by the equation F = I L × B, where I is the current, L is the length of the segment within the magnetic field, and B is the magnetic field strength. The direction of the force is given by the right-hand rule, which is essential for determining whether the force is attractive or repulsive.

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