A straight wire carrying a 3.0- A current is placed in a...

Name: Problem 24, Chapter 19: College Physics
Uploaded: 2020-03-24T21:33:13-08:00
Duration: 1 min 57 s
Channel: Zachary Warner
Description: A straight wire carrying a 3.0- A current is placed in a uniform magnetic field of magnitude 0.28 T directed perpendicular to the wire. (a) Find the magnitude of the magnetic force on a section of the wire having a length of 14 cm. (b) Explain why you can’t determine the direction of the magnetic force from the information given in the problem.

A straight wire carrying a 3.0- A current is placed in a uniform magnetic field of magnitude 0.28 T directed perpendicular to the wire. (a) Find the magnitude of the magnetic force on a section of the wire having a length of 14 cm. (b) Explain why you can’t determine the direction of the magnetic force from the information given in the problem.

Key Concepts

Requirement of Complete Vector Information for Direction

Determining the exact direction of the magnetic force also requires detailed information about the orientation of both the current flow and the magnetic field. Even though the problem specifies that the magnetic field is perpendicular to the wire, without a clear statement of the current's direction along the wire, it is impossible to definitively apply the right-hand rule to determine the force direction. This highlights the importance of complete vector information in magnetic force problems.

Cross Product and Right-Hand Rule

The magnetic force arises from the cross product of the current direction vector and the magnetic field vector. The magnitude of the force depends on the sine of the angle between these two directions, and the right-hand rule provides a method to determine the direction of the force. This rule involves orienting the fingers of the right hand in the direction of the current and curling them toward the direction of the magnetic field so that the thumb points in the direction of the force.

Magnetic Force on a Current-Carrying Conductor

This concept involves the force exerted on a conductor that carries electric current when it is placed in a magnetic field. The force is calculated using the equation F = I L B sin(?), where I is the current in the conductor, L is the length of the conductor within the magnetic field, B is the magnetic field strength, and ? is the angle between the current direction and the magnetic field. This principle is foundational in understanding devices like electric motors and generators.

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