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184_notes:dist_charges [2021/02/13 19:17] – bartonmo | 184_notes:dist_charges [2021/02/13 19:21] – [Conducting Sphere of Charge] bartonmo | ||
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- | 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 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 |
$$\vec{E}_{outside}=\frac{1}{4 \pi \epsilon_0}\frac{Q}{r^2}\hat{r}$$ | $$\vec{E}_{outside}=\frac{1}{4 \pi \epsilon_0}\frac{Q}{r^2}\hat{r}$$ | ||
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:// | This is actually the primary idea behind shielding sensitive electronics (also referred to as a [[https:// |