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6. Positive charge Q is distributed uniformly along the x-axis. Find the electric potential at the origin in the figure. Draw dą, dx, and in the figure. You must use the given symbols. Do not change them. Use dV=kdq/r

6. Positive charge Q is distributed uniformly along the x-axis. Find the electric potential at the origin in the figure. Draw dą, dx, and in the figure. You must use the given symbols. Do not change them. Use dV=kdq/r

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6. Positive charge \( Q \) is distributed uniformly along the \( x \)-axis. Find the electric potential at the origin in the figure. Draw \( dq \), \( dx \), and in the figure. You must use the given symbols. Do not change them. Use \( dV = k \frac{dq}{r} \). --- **Diagram Explanation:** - The diagram shows a line segment along the \( x \)-axis representing a uniformly distributed positive charge \( Q \). - The line starts from point \( a \) on the \( x \)-axis and extends to a length \( L \). - The point of interest for calculating the electric potential is at the origin (0 on the \( x \)-axis). - The charge is distributed along the segment between \( a \) and \( a+L \). **Key Symbols in the Diagram:** - \( Q \): Represents the total positive charge uniformly distributed. - \( x \): A variable used along the \( x \)-axis. - \( a \): The starting point of the charge distribution along the \( x \)-axis. - \( L \): The length over which the charge is distributed. - \( dq \): An infinitesimal element of charge. - \( dx \): An infinitesimal segment of the length along the \( x \)-axis. - \( r \): Represents the distance from the charge element \( dq \) at position \( x \) to the origin. The task involves setting up the expression for electric potential using these elements and integrating accordingly.
Transcribed Image Text:6. Positive charge \( Q \) is distributed uniformly along the \( x \)-axis. Find the electric potential at the origin in the figure. Draw \( dq \), \( dx \), and in the figure. You must use the given symbols. Do not change them. Use \( dV = k \frac{dq}{r} \). --- **Diagram Explanation:** - The diagram shows a line segment along the \( x \)-axis representing a uniformly distributed positive charge \( Q \). - The line starts from point \( a \) on the \( x \)-axis and extends to a length \( L \). - The point of interest for calculating the electric potential is at the origin (0 on the \( x \)-axis). - The charge is distributed along the segment between \( a \) and \( a+L \). **Key Symbols in the Diagram:** - \( Q \): Represents the total positive charge uniformly distributed. - \( x \): A variable used along the \( x \)-axis. - \( a \): The starting point of the charge distribution along the \( x \)-axis. - \( L \): The length over which the charge is distributed. - \( dq \): An infinitesimal element of charge. - \( dx \): An infinitesimal segment of the length along the \( x \)-axis. - \( r \): Represents the distance from the charge element \( dq \) at position \( x \) to the origin. The task involves setting up the expression for electric potential using these elements and integrating accordingly.
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