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| 184_notes:moving_q [2018/02/23 02:03] – dmcpadden | 184_notes:moving_q [2018/07/03 03:40] – [Magnetic Field Equation for a Moving Point Charge] curdemma | ||
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| Section 17.3 in Matter and Interactions (4th edition) | Section 17.3 in Matter and Interactions (4th edition) | ||
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| ===== Moving Charges Make Magnetic Fields ===== | ===== Moving Charges Make Magnetic Fields ===== | ||
| Just like we did with electric fields, we will start with magnetic fields by looking at the simplest source: a single moving point charge. When we are talking about this moving charge and the corresponding magnetic field, there are intuitive qualities that we want to make sure our mathematical model includes: (1) the farther away the observation point is from the moving charge, the smaller that we expect the magnetic field to be; (2) the larger the amount of charge, the larger we expect the magnetic field to be; and (3) the faster the charge is moving, the larger we expect the magnetic field to be. The final piece that is perhaps not so intuitive is that the direction of the magnetic field is actually perpendicular to observation point and to the velocity vector. However, each of these demands is consistent with experimental observations of moving charges. These notes will detail the mathematical equation that we use for the magnetic field (only for a single moving point charge) and explain a new tool called the [[184_notes: | Just like we did with electric fields, we will start with magnetic fields by looking at the simplest source: a single moving point charge. When we are talking about this moving charge and the corresponding magnetic field, there are intuitive qualities that we want to make sure our mathematical model includes: (1) the farther away the observation point is from the moving charge, the smaller that we expect the magnetic field to be; (2) the larger the amount of charge, the larger we expect the magnetic field to be; and (3) the faster the charge is moving, the larger we expect the magnetic field to be. The final piece that is perhaps not so intuitive is that the direction of the magnetic field is actually perpendicular to observation point and to the velocity vector. However, each of these demands is consistent with experimental observations of moving charges. These notes will detail the mathematical equation that we use for the magnetic field (only for a single moving point charge) and explain a new tool called the [[184_notes: | ||
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| ==== Magnetic Field Equation for a Moving Point Charge ==== | ==== Magnetic Field Equation for a Moving Point Charge ==== | ||
| - | The general equation for the magnetic field ($\vec{B}$) at some Point P due to a moving charge is given by: | + | The general equation for the magnetic field ($\vec{B}$), with units of Tesla ($T$), |
| $$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \hat{r}}{r^2}$$ | $$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \hat{r}}{r^2}$$ | ||
| which you may hear referred to as the [[https:// | which you may hear referred to as the [[https:// | ||