A line charge lies on the x-axis between x = -L and x = 0. The line charge has nonuniform linear charge density λ(x) = x/L. 2(x) y P2 P1 x = -L (a) Find the electric potential at point P₁, a distance x to the right of the line charge. (b) Find the electric potential at point Po, a distance y above the right end of the line
A line charge lies on the x-axis between x = -L and x = 0. The line charge has nonuniform linear charge density λ(x) = x/L. 2(x) y P2 P1 x = -L (a) Find the electric potential at point P₁, a distance x to the right of the line charge. (b) Find the electric potential at point Po, a distance y above the right end of the line
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![**Problem 6: Line Charge and Electric Potential**
A line charge lies on the x-axis between \( x = -L \) and \( x = 0 \). The line charge has a nonuniform linear charge density given by:
\[
\lambda(x) = \lambda_0 \frac{x}{L}
\]
**Diagram Description:**
The diagram illustrates a line charge located along the x-axis starting from \( x = -L \) to \( x = 0 \). The line is marked in blue and labeled with the linear charge density \( \lambda(x) \). Two points, \( P_1 \) and \( P_2 \), are marked on the graph:
- \( P_1 \) is located at a distance \( x \) to the right of the end of the line charge on the x-axis.
- \( P_2 \) is positioned vertically above the right end of the line charge, at a distance \( y \) on the y-axis.
**Questions:**
(a) Find the electric potential at point \( P_1 \), a distance \( x \) to the right of the line charge.
(b) Find the electric potential at point \( P_2 \), a distance \( y \) above the right end of the line charge.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F216015d9-daff-4e98-b3d1-7f3f5202e820%2F254150bf-6fee-415a-95de-7d1c7e3035db%2Frl1rzve_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 6: Line Charge and Electric Potential**
A line charge lies on the x-axis between \( x = -L \) and \( x = 0 \). The line charge has a nonuniform linear charge density given by:
\[
\lambda(x) = \lambda_0 \frac{x}{L}
\]
**Diagram Description:**
The diagram illustrates a line charge located along the x-axis starting from \( x = -L \) to \( x = 0 \). The line is marked in blue and labeled with the linear charge density \( \lambda(x) \). Two points, \( P_1 \) and \( P_2 \), are marked on the graph:
- \( P_1 \) is located at a distance \( x \) to the right of the end of the line charge on the x-axis.
- \( P_2 \) is positioned vertically above the right end of the line charge, at a distance \( y \) on the y-axis.
**Questions:**
(a) Find the electric potential at point \( P_1 \), a distance \( x \) to the right of the line charge.
(b) Find the electric potential at point \( P_2 \), a distance \( y \) above the right end of the line charge.
Expert Solution
Step 1
(a) The linear charge density is
The electric field is directed away from positive charge and is towards the negative charge.
Let there be an element, , the electric field at point is away from it.
The diagram is
The electric field at point is
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