A long wire carrying a 6.00 - A current reverses direc- tion...

A long wire carrying a $6.00 - A$ current reverses direc- tion by means of two right angle bends, as shown in Fig. P27.75. The part of the wire where the bend occurs is in a magnetic field of 0.666$\mathrm { T }$ confined to the circular region of diameter $75 \mathrm { cm } ,$ as shown. Find the magnitude and direction of the net force that the magnetic field exerts on this wire.

A long wire carrying a $6.00 - A$ current reverses direc-
tion by means of two right angle bends, as shown in Fig.
P27.75. The part of the wire
where the bend occurs is in a magnetic field of 0.666$\mathrm { T }$ confined to the circular region of
diameter $75 \mathrm { cm } ,$ as shown. Find
the magnitude and direction of
the net force that the magnetic
field exerts on this wire.

Key Concepts

Magnetic Field

The magnetic field represents the region in which a magnetic force can be experienced by moving charges or magnetic materials. Its strength and orientation at various points in space determine the magnitude and direction of the force on a current-carrying wire. Understanding magnetic fields is crucial in the study of electromagnetism and for practical applications in devices like motors and generators.

Vector Addition of Forces

When a conductor has multiple segments each experiencing a magnetic force, the net force on the conductor is found by adding these individual forces as vectors. This concept involves calculating both the magnitude and the direction of each force component and then determining the resultant force acting on the entire system.

Magnetic Force on a Current-Carrying Conductor

This concept describes the force experienced by a wire when it carries an electric current through a magnetic field. The force is determined using the relationship F = I (L x B), where the cross product indicates that the force is perpendicular to both the current direction and the magnetic field. This principle is central in understanding how currents interact with magnetic fields in various applications.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the magnetic force acting on a current-carrying conductor. By aligning the fingers of your right hand with the current and curling them toward the magnetic field, your thumb points in the direction of the resulting force. This tool is essential for visualizing and predicting the behavior of magnetic forces in experiments and applications.

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