Answered: 2q d +-x 2d d

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter8: Electricity And Magnetism

Section: Chapter Questions

Problem 1SA

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Two positive charges each of charge q are fixed on the y-axis, one at

y = d

and the other at

y = −d

as in the figure shown below. A third positive charge 2q located on the x-axis at

x = 2d

is released from rest.

Three positive charges lie along the axes of an x y-coordinate plane.

Charge q lies a distance d above the origin.
Charge q lies a distance d below the origin.
Charge 2q lies a distance 2d to the right of the origin.

(a) Find a symbolic expression for the total electric potential due to the first two charges at the location of the charge 2q. (Use any variable or symbol stated above along with the following as necessary: k_e for the Coulomb constant.)

V =

(b) Find a symbolic expression for the electric potential energy of the charge 2q. (Use any variable or symbol stated above along with the following as necessary: k_e for the Coulomb constant.)

PE =

4keq2√5d

(c) Find a symbolic expression for the kinetic energy of the charge 2q after it has moved infinitely far from the other charges. (Use any variable or symbol stated above along with the following as necessary: k_e for the Coulomb constant.)

KE =

(d) Find a symbolic expression for the speed of the charge 2q after it has moved infinitely far from the other charges if its mass is m. (Use any variable or symbol stated above along with the following as necessary: k_e for the Coulomb constant.)

v =

The diagram shows a coordinate system with charges placed at specific points. It consists of:

1. **Coordinate Axes**:
- The vertical axis is labeled \(y\).
- The horizontal axis is labeled \(x\).

2. **Charges**:
- **Charge \(q\)**:
- Positioned at a distance \(d\) above the origin on the \(y\)-axis.
- Positioned at a distance \(d\) below the origin on the \(y\)-axis.
- **Charge \(2q\)**:
- Positioned at a distance \(2d\) along the positive \(x\)-axis from the origin.

3. **Visual Representation**:
- Each charge is marked with a plus sign indicating positive charge.
- Charges are depicted as orange circles with a "+" symbol inside.

The arrangement of charges suggests this may be an example used in electrostatics to demonstrate concepts like electric fields or potential due to point charges.

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