The infinite, straight wire shown in the accompanying figure...

The infinite, straight wire shown in the accompanying figure carries a current $I_{1} .$ The rectangular loop, whose long sides are parallel to the wire, carries a current $I_{2}$ What are the magnitude and direction of the force on the rectangular loop due to the magnetic field of the wire?

The infinite, straight wire shown in the accompanying figure carries a current $I_{1} .$ The rectangular loop, whose long sides are parallel to the wire, carries a current $I_{2}$
What are the magnitude and direction of the force on the rectangular loop due to the magnetic field of the wire?

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Key Concepts

Magnetic Field from a Straight Conductor

This concept refers to the magnetic field generated by a long, current-carrying wire. The field forms concentric circles around the wire, and its magnitude at a distance r is given by B = (?? I)/(2?r). This result is derived using Ampère’s law, illustrating that the field decreases inversely with distance from the wire.

Magnetic Force on a Current-Carrying Conductor

This concept involves the force experienced by a segment of a conductor carrying current when placed in an external magnetic field. According to the formula F = I (L × B), the force is determined by the vector cross product of the current element and the magnetic field. This principle is essential in understanding how forces arise in systems like current loops and electric motors.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of magnetic field lines around a current and the direction of the force on a current element. When applying the rule to a current-carrying wire, pointing the thumb in the direction of current flow will cause the fingers to curl in the direction of the magnetic field, while a similar approach helps establish the force direction from the cross product in the magnetic force equation.

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