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184_notes:examples:week4_two_segments [2018/02/03 21:21] – [Solution] tallpaul | 184_notes:examples:week4_two_segments [2021/05/25 14:28] (current) – schram45 | ||
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===== Example: Two Segments of Charge ===== | ===== Example: Two Segments of Charge ===== | ||
Suppose we have two segments of uniformly distributed charge, one with total charge $+Q$, the other with $-Q$. The two segments each have length $L$, and lie crossed at their endpoints in the $xy$-plane. The segment with charge $+Q$ lies along the $y$-axis, and the segment with charge $-Q$ lies along the $x$-axis. See below for a diagram of the situation. Create an expression for the electric field $\vec{E}_P$ at a point $P$ that is located at $\vec{r}_P=r_x\hat{x}+r_y\hat{y}$. You don't have to evaluate integrals in the expression. | Suppose we have two segments of uniformly distributed charge, one with total charge $+Q$, the other with $-Q$. The two segments each have length $L$, and lie crossed at their endpoints in the $xy$-plane. The segment with charge $+Q$ lies along the $y$-axis, and the segment with charge $-Q$ lies along the $x$-axis. See below for a diagram of the situation. Create an expression for the electric field $\vec{E}_P$ at a point $P$ that is located at $\vec{r}_P=r_x\hat{x}+r_y\hat{y}$. You don't have to evaluate integrals in the expression. | ||
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* Use $\lambda$ to write an expression for $\text{d}Q$. | * Use $\lambda$ to write an expression for $\text{d}Q$. | ||
* Assign a variable location to the $\text{d}Q$ piece, and then use that location to find the separation vector, $\vec{r}$. | * Assign a variable location to the $\text{d}Q$ piece, and then use that location to find the separation vector, $\vec{r}$. | ||
- | * Write an expression for \text{d}\vec{E}. | + | * Write an expression for $\text{d}\vec{E}$. |
* Figure out the bounds of the integral, and integrate to find electric field at $P$. | * Figure out the bounds of the integral, and integrate to find electric field at $P$. | ||
* Repeat the above steps for the other segment of charge. | * Repeat the above steps for the other segment of charge. | ||
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Because we know that electric fields add through superposition, | Because we know that electric fields add through superposition, | ||
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+ | <WRAP TIP> | ||
+ | ===Assumption=== | ||
+ | The charge is evenly distributed along each segment of charge. This allows each little piece of charge to have the same value along each line. | ||
+ | </ | ||
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