8.6: The relationship between electric current, magnetic fields, and magnetic force
- Page ID
- 476783
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Learning Objectives
- Describe the effects of magnetic fields on moving charges.
- Use the right hand rule 1 to determine the relationship between the velocity of a charge, the direction of the magnetic field, and the direction of the magnetic force on a moving charge.
What is the mechanism by which one magnet exerts a force on another? The answer is related to the fact that all magnetism is caused by current, the flow of charge. Magnetic fields exert forces on moving charges, and so they exert forces on other magnets, all of which have moving charges. However, unlike most forces that we have examined in this course, the relationship between the direction of the moving charge and the magnetic force applied by it are not intuitive. We will examine this connection briefly, but not in a great deal of detail. In a more advanced physics text you would be using the rules for vectors to perform calculations to find the relationship between the moving charge and the applied force. For this text we only want to understanding a little bit about how the direction is important in order to understand the ensuing phenomena.
MAKING CONNECTIONS: CHARGES AND MAGNETS
There is no magnetic force on static charges. However, there is a magnetic force on moving charges. When charges are stationary, their electric fields do not affect magnets. But, when charges move, they produce magnetic fields that exert forces on other magnets. When there is relative motion, a connection between electric and magnetic fields emerges—each affects the other.
Direction of Force: Right Hand Rule 1
The direction of the magnetic force \(\mathbf{F}\) is perpendicular to the plane formed by \(\mathbf{v}\) and \(\mathbf{B}\), as determined by the right hand rule 1 (or RHR-1), which is illustrated in Figure \(\PageIndex{1}\). For the purposes of this text, what you should understand about this is that the magnetic force applied by the moving charge is always perpendicular to both the direction of the moving charge and the magnetic field. The direction of the moving charge is not always perpendicular to the magnetic field, but is strongest when it is perpendicular. When the direction is parallel, the magnetic force is zero. The variation in the angle between the moving charge and the magnetic field can have some dramatic effects, as we shall soon seen. Whenever you see the RHR-1 notation or accompanying graphics in this text, simply consider the three dimensional relationship between the direction of the moving charge, the direction of the magnetic field, and the direction of the magnetic force.
Section Summary
- The maximum force a magnetic field can exert on a moving charge is
\[F=q v B \nonumber\]
- The direction of the force on a moving charge is given by right hand rule 1 (RHR-1): Point the thumb of the right hand in the direction of \(v\), the fingers in the direction of \(B\), and a perpendicular to the palm points in the direction of \(F\).
- The force is perpendicular to the plane formed by \(\mathbf{V}\) and \(\text { B }\). Since the force is zero if \(\mathbf{V}\) is parallel to \(\text { B }\), charged particles often follow magnetic field lines rather than cross them.
Glossary
- right hand rule 1 (RHR-1)
- the rule to determine the direction of the magnetic force on a positive moving charge: when the thumb of the right hand points in the direction of the charge’s velocity \(\mathbf{v}\) and the fingers point in the direction of the magnetic field \(\mathbf{B}\), then the force on the charge is perpendicular and away from the palm; the force on a negative charge is perpendicular and into the palm
- tesla
- T, the SI unit of the magnetic field strength; \(1 \mathrm{~T}=\frac{1 \mathrm{~N}}{\mathrm{~A} \cdot \mathrm{m}}\)
- magnetic force
- the force on a charge produced by its motion through a magnetic field
- gauss
- G, the unit of the magnetic field strength; \(1 \mathrm{G}=10^{-4} \mathrm{~T}\)