---### 4: The Electric Field of Distributed Charges#### 4.4.2 Electric Field Near the Center of a Uniform DiskAnother special case turns out to be of considerable interest. Let's see what the electric field is like near the center of a uniformly charged disk (x small, but not zero, for the reasons just given). Suppose that we are so close to the disk that \( x \) is very small (\( x \ll R \)), or equivalently that we are some distance away but the disk is very large (\( R \gg x \)).\[ \text{Show that near the disk } E = \frac{Q/A}{2 \varepsilon_0} \left[1 - \frac{x}{R}\right]. \]---This section is designed to help students understand the behavior of the electric field near the center of a uniformly charged disk. The conditions being analyzed are that the distance \( x \) from the center of the disk is much smaller than the radius \( R \) of the disk, indicating either a small \( x \) or a large \( R \). This specific scenario leads to an approximation for the electric field close to the center. The students are required to show the given formula through appropriate derivations and explanations.

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Another special case turns out to be of considerable interest. Let's see what the electric field is like near the center of a uniformly charged disk (x small, but not zero, for the reasons just given). Suppose that we are so close to the disk that x is very small (x <> x). QIA Show that near the disk E- R

Another special case turns out to be of considerable interest. Let's see what the electric field is like near the center of a uniformly charged disk (x small, but not zero, for the reasons just given). Suppose that we are so close to the disk that x is very small (x <> x). QIA Show that near the disk E- R

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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### 4: The Electric Field of Distributed Charges

#### 4.4.2 Electric Field Near the Center of a Uniform Disk

Another special case turns out to be of considerable interest. Let's see what the electric field is like near the center of a uniformly charged disk (x small, but not zero, for the reasons just given). Suppose that we are so close to the disk that \( x \) is very small (\( x \ll R \)), or equivalently that we are some distance away but the disk is very large (\( R \gg x \)).

\[
\text{Show that near the disk } E = \frac{Q/A}{2 \varepsilon_0} \left[1 - \frac{x}{R}\right].
\]

---
This section is designed to help students understand the behavior of the electric field near the center of a uniformly charged disk. The conditions being analyzed are that the distance \( x \) from the center of the disk is much smaller than the radius \( R \) of the disk, indicating either a small \( x \) or a large \( R \). This specific scenario leads to an approximation for the electric field close to the center. The students are required to show the given formula through appropriate derivations and explanations.

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