A line of positive charge is formed into a semicircle of radius R = 57.0 cm as shown in the figure. The charge per unit length along the semicircle is described by the expression λ = λ0 sinθ, λ0 = 14.0 μC/m. Calculate the electric field at the center of curvature. (Here, θ = 0 on the y-axis, increasing clockwise (CW)). The image depicts a semicircular arc with radius \( R \) centered at the origin of a coordinate plane. The semicircle is positioned above the x-axis, and the y-axis bisects it.Key features of the diagram:1. **Axes**: - The x-axis runs horizontally. - The y-axis runs vertically and passes through the center of the semicircle.2. **Semicircle**: - The semicircle is part of a circle with radius \( R \). - It is centered at the origin (0,0).3. **Radius \( R \)**: - The radius \( R \) extends from the origin to any point on the arc.4. **Angle \( \theta \)**: - The angle \( \theta \) is formed between the radius \( R \) and the y-axis. - This represents the angle in polar coordinates used to define a point on the semicircle.This diagram is typically used to illustrate concepts in trigonometry, polar coordinates, or integrals in calculus.

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A line of positive charge is formed into a semicircle of radius R = 57.0 cm as shown in the figure. The charge per unit length along the semicircle is described by the expression λ = λ0 sinθ, λ0 = 14.0 μC/m. Calculate the electric field at the center of curvature. (Here, θ = 0 on the y-axis, increasing clockwise (CW)).

The image depicts a semicircular arc with radius \( R \) centered at the origin of a coordinate plane. The semicircle is positioned above the x-axis, and the y-axis bisects it.

Key features of the diagram:

1. **Axes**:
- The x-axis runs horizontally.
- The y-axis runs vertically and passes through the center of the semicircle.

2. **Semicircle**:
- The semicircle is part of a circle with radius \( R \).
- It is centered at the origin (0,0).

3. **Radius \( R \)**:
- The radius \( R \) extends from the origin to any point on the arc.

4. **Angle \( \theta \)**:
- The angle \( \theta \) is formed between the radius \( R \) and the y-axis.
- This represents the angle in polar coordinates used to define a point on the semicircle.

This diagram is typically used to illustrate concepts in trigonometry, polar coordinates, or integrals in calculus.

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