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| 184_notes:moving_q [2017/10/24 01:11] – dmcpadden | 184_notes:moving_q [2018/02/23 02:03] – dmcpadden |
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| We could also get this result using the [[184_notes:rhr|Right Hand Rule]], which says that if you point your fingers in the direction of the first vector (the velocity vector in this case) and curl the towards the direction of the second vector (the separation vector in this case), your thumb will point in the direction of the cross product (or the B-field direction here). If you do this - point your right hand fingers in the direction of +x and curl them toward +y direction, your thumb will point in the +z direction or out of the page. **NOTE: the right hand rule is true for POSITIVE charges**. If you have a negative charge, you can //either// use your left hand or just flip the direction of your final vector (i.e. if you get +z for your right hand rule, you would have a direction of -z for a negative charge). | We could also get this result using the [[184_notes:rhr|Right Hand Rule]], which says that if you point your fingers in the direction of the first vector (the velocity vector in this case) and curl the towards the direction of the second vector (the separation vector in this case), your thumb will point in the direction of the cross product (or the B-field direction here). If you do this - point your right hand fingers in the direction of +x and curl them toward +y direction, your thumb will point in the +z direction or out of the page. **NOTE: the right hand rule is true for POSITIVE charges**. If you have a negative charge, you can //either// use your left hand or just flip the direction of your final vector (i.e. if you get +z for your right hand rule, you would have a direction of -z for a negative charge). |
| ==== Superposition ==== | |
| {{ 184_notes:Week9_3.png?200}} | |
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| Superposition is central to understanding of all E&M fields and governs how all of these fields add up. That is, magnetic field vectors superpose just as you might expect. This means that if you have two moving charges, the magnetic field at any given point is given by the vector addition of the magnetic field due to one of the moving charges //plus// the magnetic field due to the other moving charge. | |
| $$\vec{B}_{total}=\vec{B}_1+\vec{B}_2$$ | |
| This idea scales for as many moving charges as you have: | |
| $$\vec{B}_{total}=\vec{B}_1+\vec{B}_2+\vec{B}_3+\vec{B}_4+...$$ | |
| However, if you have both electric and magnetic fields you **cannot** just add together the magnetic and electric fields. These are different quantities with different units; therefore, they do not add together (this would be like trying to add time to mass - it's just not a thing you can do). | |
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| {{youtube>dZxoWgE1Hb4?large}} | |
| ==== Examples ==== | ==== Examples ==== |
| [[:184_notes:examples:Week9_detecting_b|Magnetic Field near a Moving Charge]] | [[:184_notes:examples:Week9_detecting_b|Magnetic Field near a Moving Charge]] |