184_notes:dist_charges

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184_notes:dist_charges [2021/02/13 19:17] – bartonmo184_notes:dist_charges [2021/02/13 19:26] (current) – [Insulating Cylinder of Charge] bartonmo
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 [{{  184_notes:conductorsphereefield.png?200|Electric Field inside and around a conductor}}]  [{{  184_notes:conductorsphereefield.png?200|Electric Field inside and around a conductor}}] 
-Outside the metal ball, we would hypothesize that the electric field should point in towards the metal ball since the electric field points toward a negative point charge. If you actually do the math (either with an integral over the volume of the sphere or with a computational code), you will see exactly this. The electric field will point radially towards the metal ball and get stronger the closer you are to the ball. In fact, if you are looking for the electric field outside the metal ball, it will look exactly the same as if there were a point charge (with the same net negative charge) at the center of the ball. Thus, //__outside a conducting sphere__// we can still use the equation:+Outside the metal ball, we would hypothesize that the electric field should point in towards the metal ball since the electric field points toward a negative point charge. If you actually do the math (either with an integral over the volume of the sphere or with a computational code), you will see exactly this. The electric field will point radially towards the metal ball and get stronger the closer you are to the ball. In fact, if you are looking for the electric field outside the metal ball, it will look exactly the same as if there were a point charge (with the same net negative charge) at the center of the ball. **Thus, outside a conducting sphere we can still use the equation:**
 $$\vec{E}_{outside}=\frac{1}{4 \pi \epsilon_0}\frac{Q}{r^2}\hat{r}$$ $$\vec{E}_{outside}=\frac{1}{4 \pi \epsilon_0}\frac{Q}{r^2}\hat{r}$$
 where $Q$ is the total charge on the ball and $\vec{r}$ points from the center of the sphere to the observation location. where $Q$ is the total charge on the ball and $\vec{r}$ points from the center of the sphere to the observation location.
  
-However, what would happen to the electric field inside the sphere? We know that all of the charges should be located on the surface of the metal ball. When inside the sphere, there will always be a contribution to the electric field from the electrons on one side of the sphere that opposes the electric field contribution from the electrons on the other side of sphere. This means that on the inside, the electric field from the electrons on the surface perfectly cancels out, leaving a net field of zero. +However, what would happen to the electric field inside the sphere? We know that all of the charges should be located on the surface of the metal ball. When inside the sphere, there will always be a contribution to the electric field from the electrons on one side of the sphere that opposes the electric field contribution from the electrons on the other side of sphere. This means that on the inside, the electric field from the electrons on the surface perfectly cancels out,** leaving a net field of zero.** 
 $$\vec{E}_{inside}=0$$ $$\vec{E}_{inside}=0$$
 This is actually the primary idea behind shielding sensitive electronics (also referred to as a [[https://en.wikipedia.org/wiki/Faraday_cage|Faraday Cage]]). If you surround something with a sheet of charged metal, then you can guarantee that there will be no electric field on the inside. This net electric field inside of the cage is a result of the superposition of the applied external field and the field generated by the cage material, the cage is not "blocking the field." This is actually the primary idea behind shielding sensitive electronics (also referred to as a [[https://en.wikipedia.org/wiki/Faraday_cage|Faraday Cage]]). If you surround something with a sheet of charged metal, then you can guarantee that there will be no electric field on the inside. This net electric field inside of the cage is a result of the superposition of the applied external field and the field generated by the cage material, the cage is not "blocking the field."
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 Just like with the sphere, if we are outside the cylinder, the electric field will look the same as if the cylinder were a conductor (as long as it has the same amount of charge). Namely that it points radially away from the positively charged cylinder, expect near the ends of the cylinder. Just like with the sphere, if we are outside the cylinder, the electric field will look the same as if the cylinder were a conductor (as long as it has the same amount of charge). Namely that it points radially away from the positively charged cylinder, expect near the ends of the cylinder.
  
-Inside the insulating cylinder, the electric field would be non-zero. The contributions to the electric field from the charges in the middle of the cylinder do not completely cancel out, leaving an electric field that points away from the center of the cylinder for a positive charge (it would point towards the center for a negative charge). The electric field inside will be strongest at the edge of the cylinder and will be smallest (or exactly zero) in the center.+Inside the insulating cylinder, the electric field would be non-zero. The contributions to the electric field from the charges in the middle of the cylinder do not completely cancel out, leaving an electric field that points away from the center of the cylinder for a positive charge (it would point towards the center for a negative charge). **The electric field inside will be strongest at the edge of the cylinder and will be smallest (or exactly zero) in the center.**
 [{{184_notes:insulatorcylinderefield.png?125|Electric field inside and around a cylindrical insulator  }}] [{{184_notes:insulatorcylinderefield.png?125|Electric field inside and around a cylindrical insulator  }}]
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