### Problem 5: Electric Potential of Uniformly Charged RodIn the given problem, a plastic rod with a uniformly distributed charge \( Q = -27.7 \) pC has been shaped into a circular arc. The arc has a radius of \( 4.69 \) cm and subtends a central angle of \( 120^\circ \). Considering that the electric potential \( V \) is zero at infinity, the task is to determine the electric potential in volts at point \( P \), which is the center of curvature of the rod.#### Diagram Explanation:The diagram shows:1. A circular arc of charge \( Q \), indicated by the orange, bent plastic rod.2. The point \( P \) is marked as the central point of curvature of the circular arc.3. The radius \( R \), which is \( 4.69 \) cm, is the distance from \( P \) to any point on the rod.4. The angle \( \phi \) refers to the angular position along the arc, spanning a total central angle of \( 120^\circ \) (which is equivalent to \( \frac{2\pi}{3} \) radians). #### Multiple Choice Answers:(a) -5.12 V(b) -4.86 V(c) -5.31 V(d) -5.42 V(e) None of the above#### Objective:To find the electric potential \( V \) at point \( P \) in volts.**Reminder:** The charge distributed along the arc and curvature must be considered to calculate the electric potential.---This problem helps to understand the principles of electric potential due to continuous charge distributions, especially in geometrical configurations like arcs. Be sure to apply the principles of superposition and integration over the arc for the correct solution.

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In the figure a plastic rod having a uniformly distributed charge Q = -27.7 pC has been bent into a circular arc of radius 4.69 cm and central angle 120°. With V = 0 at infinity, what is the electric potential in volts at P, the center of curvature of the rod? 5. R (a) -5.12 V (b) -4.86 V (c) -5.31 V (d) -5.42 V (e) None of the above

In the figure a plastic rod having a uniformly distributed charge Q = -27.7 pC has been bent into a circular arc of radius 4.69 cm and central angle 120°. With V = 0 at infinity, what is the electric potential in volts at P, the center of curvature of the rod? 5. R (a) -5.12 V (b) -4.86 V (c) -5.31 V (d) -5.42 V (e) None of the above

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

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.

Question

### Problem 5: Electric Potential of Uniformly Charged Rod

In the given problem, a plastic rod with a uniformly distributed charge \( Q = -27.7 \) pC has been shaped into a circular arc. The arc has a radius of \( 4.69 \) cm and subtends a central angle of \( 120^\circ \). Considering that the electric potential \( V \) is zero at infinity, the task is to determine the electric potential in volts at point \( P \), which is the center of curvature of the rod.

#### Diagram Explanation:

The diagram shows:

1. A circular arc of charge \( Q \), indicated by the orange, bent plastic rod.
2. The point \( P \) is marked as the central point of curvature of the circular arc.
3. The radius \( R \), which is \( 4.69 \) cm, is the distance from \( P \) to any point on the rod.
4. The angle \( \phi \) refers to the angular position along the arc, spanning a total central angle of \( 120^\circ \) (which is equivalent to \( \frac{2\pi}{3} \) radians).

#### Multiple Choice Answers:

(a) -5.12 V

(b) -4.86 V

(c) -5.31 V

(d) -5.42 V

(e) None of the above

#### Objective:

To find the electric potential \( V \) at point \( P \) in volts.

**Reminder:** The charge distributed along the arc and curvature must be considered to calculate the electric potential.

---

This problem helps to understand the principles of electric potential due to continuous charge distributions, especially in geometrical configurations like arcs. Be sure to apply the principles of superposition and integration over the arc for the correct solution.

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