Numerade

University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

ISBN #9780072857368

1st Edition

3,117 Questions

54,786 Students Helped

Summary

This section covers the generation of magnetic fields by moving charges and current distributions, starting with the Biot–Savart Law, which provides the differential contribution from a current element, and Ampère’s Law, which greatly simplifies calculations in symmetric situations. Detailed analyses are given for magnetic fields from long straight wires, loops, solenoids, and toroids. The material also explains the magnetic properties of atoms and materials, including diamagnetism, paramagnetism, and ferromagnetism, and touches on effects such as eddy currents and the Meissner effect in superconductors. Understanding these principles is critical for designing electromagnets, rail guns, MRI machines, and other devices relying on magnetic fields.

Learning Objectives

Key Concepts

CONCEPT

DEFINITION

Definition: The study of the structure and behavior of atoms, from the early Bohr model to the complete quantum mechanical treatment of the hydrogen atom and multi?electron systems.

The study of the structure and behavior of atoms, from the early Bohr model to the complete quantum mechanical treatment of the hydrogen atom and multi?electron systems. •

Example 1

Two long, straight wires are parallel to each other. The wires carry currents of different magnitudes. If the amount of current flowing in each wire is doubled, the magnitude of the force between the wires will be a) twice the magnitude of the original force. b) four times the magnitude of the original force. c) the same as the magnitude of the original force. d) half of the magnitude of the original force.

Example 2

A current element produces a magnetic field in the region surrounding it. At any point in space, the magnetic field produced by this current element points in a direction that is a) radial from the current element to the point in space. b) parallel to the current element. c) perpendicular to the current element and to the radial direction.

Example 4

The magnetic force cannot do work on a charged particle since the force is always perpendicular to the velocity. How then can magnets pick up nails? Consider two parallel current-carrying wires. The magnetic fields cause attractive forces between the wires, so it appears that the magnetic field due to one wire is doing work on the other wire. How is this explained? a) The magnetic force can do no work on isolated charges; this says nothing about the work it can do on charges confined in a conductor. b) Since only an electric field can do work on charges, it is actually the electric fields doing the work here. c) This apparent work is due to another type of force.

Example 5

In a solenoid in which the wires are wound such that each loop touches the adjacent ones, which of the following will increase the magnetic field inside the magnet? a) making the radius of the loops smaller b) increasing the radius of the wire c) increasing the radius of the solenoid d) decreasing the radius of the wire e) immersion of the solenoid in gasoline