A current I 5 15 A is directed along the positive x

Name: Problem 23, Chapter 19: College Physics
Uploaded: 2020-03-24T21:28:39-08:00
Duration: 2 min 42 s
Channel: Zachary Warner
Description: A current I 5 15 A is directed along the positive x - axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.12 N/m acts on the conductor in the negative y - direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.

A current I 5 15 A is directed along the positive x - axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.12 N/m acts on the conductor in the negative y - direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.

Key Concepts

Calculation of Magnetic Field Magnitude

Using the simplified expression for the magnetic force per unit length, F/L = I B sin(?), where ? is the angle between the current and the magnetic field (often 90° for a perpendicular arrangement), the magnitude of the magnetic field can be isolated as B = (F/L) / (I sin ?). With the sine of 90° being one, this formula allows for a straightforward calculation of the magnetic field's strength when the force per unit length and the current are known.

Lorentz Force Law

This law states that a current-carrying conductor in a magnetic field experiences a force proportional to the current, the length of the conductor, and the magnetic field, and is given by F = I (L × B). The cross product sign indicates that the force is perpendicular to both the current direction and the magnetic field. It is a foundational concept in electromagnetism that describes how magnetic fields interact with moving charges.

Cross Product and Right-Hand Rule

The cross product in the Lorentz force formula determines the direction of the force. By aligning the fingers of the right hand along the current direction (or segment of the conductor) and curling them toward the direction of the magnetic field, the thumb points in the direction of the force. This method, known as the right-hand rule, is crucial for determining the spatial orientation of magnetic forces in three-dimensional space.

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