Book cover for Introduction to Electrodynamics

Introduction to Electrodynamics

David J. Griffiths, Reed College

ISBN #9780138053260

3rd Edition

533 Questions

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Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

Magnetostatics focuses on the study of magnetic fields produced by steady currents. The key tools used in this analysis are the Biot-Savart law, which allows calculation of the field from small current elements, and Ampere's law, which simplifies magnetic field calculations in systems with high symmetry. By mastering these principles, one can solve a wide range of practical problems in electromagnetism related to electrical engineering, medical imaging, and energy conversion.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Conservation Laws:

Fundamental principles asserting that certain physical quantities—such as energy, momentum, and mass—remain constant in isolated systems.

Example Problems

Example 1

A particle of charge $q$ enters a region of uniform magnetic field $\mathbf{B}$ (pointing into the page). The field deflects the particle a distance $d$ above the original line of flight, as shown in Fig. $5.8 .$ Is the charge positive or negative? In terms of $a, d, B$ and $q,$ find the momentum of the particle.

Example 2

Find and sketch the trajectory of the particle in Ex. $5.2,$ if it starts at the origin with velocity $(a) \mathbf{v}(0)=(E / B) \hat{\mathbf{y}}$ $(b) \mathbf{v}(0)=(E / 2 B) \hat{\mathbf{y}}$ $(c) \mathbf{v}(0)=(E / B)(\hat{\mathbf{y}}+\hat{\mathbf{z}})$

Example 3

In 1897 J. J. Thomson "discovered" the electron by measuring the charge-to-mass ratio of "cathode rays" (actually, streams of electrons, with charge $q$ and mass $m$ ) as follows: (a) First he passed the beam through uniform crossed electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$ (mutually perpendicular, and both of them perpendicular to the beam), and adjusted the electric field until he got zero deflection. What, then, was the speed of the particles (in terms of $E$ and $B$ )? (b) Then he turned off the electric field, and measured the radius of curvature, $R$, of the beam. as deflected by the magnetic field alone. In terms of $E, B,$ and $R,$ what is the charge-to-mass ratio $(q / m)$ of the particles?

Example 4

Suppose that the magnetic field in some region has the form $$\mathbf{B}=k z \hat{\mathbf{x}}$$ (where $k$ is a constant). Find the force on a square loop (side $a$ ), lying in the $y z$ plane and centered at the origin, if it carries a current $I$, flowing counterclockwise, when you look down the $x$ axis.

Example 5

A current $I$ flows down a wire of radius $a$. (a) If it is uniformly distributed over the surface, what is the surface current density $K ?$ (b) If it is distributed in such a way that the volume current density is inversely proportional to the distance from the axis, what is $J ?$
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Step-by-Step Explanations

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