184_notes:dipole_sup

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184_notes:dipole_sup [2018/05/29 14:51] – [Dipole Superposition Example] curdemma184_notes:dipole_sup [2018/05/29 14:54] – curdemma
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 Once we have the electric field from the dipole, it becomes relatively simple to find the force from that dipole on any other charge that we would have near by simply by using the electric force relationship: $\vec{F}=q\vec{E}$.  Once we have the electric field from the dipole, it becomes relatively simple to find the force from that dipole on any other charge that we would have near by simply by using the electric force relationship: $\vec{F}=q\vec{E}$. 
  
-{{  184_notes:dipoleandcharge.png}}+[{{  184_notes:dipoleandcharge.png|Problem setup: $r$ vectors between the charges in the dipole and point P}}]
  
 For example, if we had a positive charge $q_3$ that was centered a distance h above our dipole (as in the first example), we could find the force on $q_3$ by using the electric field that we calculated before: For example, if we had a positive charge $q_3$ that was centered a distance h above our dipole (as in the first example), we could find the force on $q_3$ by using the electric field that we calculated before:
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 If $q_3$ happened to be negative, then the force would instead point to left (but we would not have to rewrite $\vec{E}_{net}$ because we didn't change anything about the dipole): If $q_3$ happened to be negative, then the force would instead point to left (but we would not have to rewrite $\vec{E}_{net}$ because we didn't change anything about the dipole):
 $$\vec{F}_{q_3}=-q_3\vec{E}_{net}=\frac{1}{4\pi\epsilon_0}\frac{-q_3*q}{(\sqrt{(d/2)^2+h^2})^3}\langle d, 0,0 \rangle$$ $$\vec{F}_{q_3}=-q_3\vec{E}_{net}=\frac{1}{4\pi\epsilon_0}\frac{-q_3*q}{(\sqrt{(d/2)^2+h^2})^3}\langle d, 0,0 \rangle$$
-This is often why we care about the electric field - **it doesn't matter what change about $q_3$, the electric field from the dipole is going to stay the same.** This idea will save you time when doing your calculations, especially for calculations involving more than three charges. (Since we already have the electric field for when Point P is far away from the dipole and when it is on the axis of the dipole, we could also easily find the force on $q_3$ at those locations too.)+This is often why we care about the electric field - **it doesn't matter what changes about $q_3$, the electric field from the dipole is going to stay the same.** This idea will save you time when doing your calculations, especially for calculations involving more than three charges. (Since we already have the electric field for when Point P is far away from the dipole and when it is on the axis of the dipole, we could also easily find the force on $q_3$ at those locations too.)
  
 ==== Superposition of Potential and Energy ==== ==== Superposition of Potential and Energy ====
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 Once you have the total electric potential around the dipole, it is then very easy to find the electric potential energy between a third charge ($q_3$) and the dipole: Once you have the total electric potential around the dipole, it is then very easy to find the electric potential energy between a third charge ($q_3$) and the dipole:
 $$U=q_3 V_{tot}$$ $$U=q_3 V_{tot}$$
-Again, this is often why we care about the electric potential - **it doesn't matter what change about $q_3$, the electric potential from the dipole is going to stay the same.**+Again, this is often why we care about the electric potential - **it doesn't matter what changes about $q_3$, the electric potential from the dipole is going to stay the same.**
  • 184_notes/dipole_sup.txt
  • Last modified: 2020/08/17 17:29
  • by dmcpadden