Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Fig. 24-72, two particles of charges q₁ and q₂ are fixed to an x-axis. If a third particle, of charge $+ 6.0 μC$ , is brought from an infinite distance to point P, the three-particle system has the same electric potential energy as the original two-particle system. What is the charge ratio $q_{1} / q_{2}$ ?

The charge ratio $q_{1} / q_{2}$ is -1.66.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data:

Draw the given figure as below.

Here, q₁ and q₂ are fixed charges.

The charge, $q_{3} = + 6.0 μC = + 6.0 \times 10^{- 6} C$

Step 2: Determining the concept:

Use the electric potential energy for the final three particle system,

$\begin{array}{rcl} U_{net} & = & U_{1} + U_{2} + U_{3} \\ = & \frac{1}{4 {πε}_{0}} [\frac{q_{1} q_{2}}{d} + \frac{q_{2} q_{3}}{(1.5 d)} + \frac{q_{1} q_{3}}{(2.5 d)}] \end{array}$

If two like charges (two protons or two electrons) are brought towards each other, the potential energy of the system increases. If two unlike charges i.e. a proton and an electron are brought towards each other, the electric potential energy of the system decreases.

Formulae:

The electric potential is define by,

$U_{12} = \frac{1}{4 {πε}_{0}} . \frac{q_{1} q_{2}}{d}$

The bet potential is define by,

$\begin{array}{rcl} U_{net} & = & U_{1} + U_{2} + U_{3} \end{array}$

Where, U is electric potential energy, R is distance between the point charges, q is charge, $ε_{0}$ is the permittivity of free space, and k is the Coulomb’s constant having a value

Step 3: Determining the charge ratio of

The net potential energy is,

$\begin{array}{rcl} U_{net} & = & U_{1} + U_{2} + U_{3} \\ = & \frac{1}{4 {πε}_{0}} [\frac{q_{1} q_{2}}{d} + \frac{q_{2} q_{3}}{(1.5 d)} + \frac{q_{1} q_{3}}{(2.5 d)}] \end{array}$

According to the given condition,

$\begin{array}{rcl} \frac{1}{4 {πε}_{0}} [\frac{q_{1} q_{2}}{d} + \frac{q_{2} q_{3}}{(1.5 d)} + \frac{q_{1} q_{3}}{(2.5 d)}] & = & \frac{1}{4 {πε}_{0}} . \frac{1}{d} [q_{1} q_{2}] \\ q_{1} q_{2} + \frac{q_{2} q_{3}}{1.5 d} + \frac{q_{1} q_{3}}{2.5 d} & = & q_{1} q_{2} \\ \frac{q_{2} q_{3}}{1.5 d} & = & - \frac{q_{1} q_{3}}{2.5 d} \\ \frac{q_{1}}{q_{2}} & = & - 1.66 \end{array}$

Hence, the charge ratio $q_{1} / q_{2}$ is -1.66.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data:

Step 2: Determining the concept:

Step 3: Determining the charge ratio of

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

In Fig. 24-72, two particles of charges q1 and q2 are fixed to an x-axis. If a third particle, of charge +6.0μC, is brought from an infinite distance to point P, the three-particle system has the same electric potential energy as the original two-particle system. What is the charge ratio q1/q2?

Step by Step Solution

Step 1: Given data:

Step 2: Determining the concept:

Step 3: Determining the charge ratio of

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics