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. 22-41, particle 1 of charge q₁ = -5.00q and particle 2 of charge q₂=+2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero? (b)Sketch the net electric field lines between and around the particles.

The coordinate at which the net electric field is zero is 2.72 L
The net electric field between and around the particle is sketched.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

Charge of particle 1, q₁= - 5.00q.
Charge of particle 2, q₂=+2.00 q
They are fixed on the x-axis.

Step 2: Understanding the concept of electric field

Using the concept of the electric field at a given point, we can get the value of an individual electric field by a charge. Again using the superposition law, we can get the value of the electric field in its direction and this determines the net electric field at that point. Equating the net field to zero will give to the required coordinate.

Formulae:

The magnitude of the electric field, $E = \frac{q}{4 {πε}_{o} R^{2}} \hat{R}$ (i)

where, R = The distance of field point from the charge

q = charge of the particle

According to the superposition principle, the electric field at a point due to more than one charges, data-custom-editor="chemistry" $\vec{E} = \sum_{i = 1}^{n} \vec{E_{i}} = \sum_{i = 1}^{n} \frac{q}{4 {πε}_{o} r_{i}^{2}} \hat{r_{i}}$ (ii)

Step 3: Calculation of the coordinate at which the net electric field is zero

In the region, x<0, the fields are opposite but unequal (since E₁ is everywhere bigger than E₂ in this region), so there is no possibility of cancellation of the fields. In the region between the charges 0 < x < L both the fields will add up as they point in the same direction, so net field cannot be zero. In the region x > L, the fields are opposite and unequal, so the net field in this range using equation (ii) is given as:

$\vec{E_{net}} = (|E_{2}| - |E_{1}|) \hat{i}$

Though $|q_{1}| > |q_{2}|$ , the net electric field $(E_{net})$ can be zero, since these points are closer to q₂ as compared to q₁. Thus, we look for the zero net field point in the region x > L using equation (i) as:

$\begin{array}{rcl} |\vec{E_{2}}| & = & |\vec{E_{1}}| \\ \frac{1}{4 {πε}_{o}} \frac{|q_{1}|}{x^{2}} & = & \frac{1}{4 {πε}_{o}} \frac{q_{2}}{{(x - L)}^{2}} \\ x & = & \frac{L}{1 - \sqrt{2 / 5}} \\ x & \approx & 2.72 L \end{array}$

Hence, the value of the x-coordinate is 2.72 L

Step 4: b) Sketching the electric field lines between and around the particle

the field lines around the particles are shown in the figure below:

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

In Fig. 22-41, particle 1 of charge q₁ = -5.00q and particle 2 of charge q₂=+2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero? (b)Sketch the net electric field lines between and around the particles.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of electric field

Step 3: Calculation of the coordinate at which the net electric field is zero

Step 4: b) Sketching the electric field lines between and around the particle

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. 22-41, particle 1 of charge q1 = -5.00q and particle 2 of charge q2=+2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero? (b)Sketch the net electric field lines between and around the particles.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of electric field

Step 3: Calculation of the coordinate at which the net electric field is zero

Step 4: b) Sketching the electric field lines between and around the particle

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

Famous Physicists

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

In Fig. 22-41, particle 1 of charge q₁ = -5.00q and particle 2 of charge q₂=+2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero? (b)Sketch the net electric field lines between and around the particles.