Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A thin rod of length L and total charge Q has the nonuniform CALC linear charge distribution $λ (x) = λ_{0} x / L$ , where x is measured from the rod's left end.
a. What is $λ_{0}$ in terms of Q and L ?
b. What is the electric potential on the axis at distance d left of the rod's left end?

The constant i. comes out to be $\frac{2 n}{i}$ . whereas the potential at the specified point is found to be

\frac{2 n}{4 x + 1} (1 - \frac{d}{l} \ln (1 + \frac{1}{d})\} .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Given:

A thin rod of length L and having a total charge of q, has the linear charge distribution $λ (x) = \frac{λ x}{L}$ , where x is measured from the left-end of the rod.

Formula used:

- The electric potential at a distance r from a point charge q, is givisn as:

V \frac{1}{4 π r_{0}} \frac{q}{r}

part(a) step 1: given information

(a) If we consider a small segment of length $dx$ at a distance x from left end, then charge on this segment,

d q = λ d x = \frac{λ_{0}}{L} x d x

Hence, the total charge on the rod,

Q = \int^{Q} d q = \frac{λ_{0}}{L} \int_{0}^{L} x d x = \frac{λ_{0} L}{2}

Therefore, $λ_{0} = \frac{2 Q}{L}$

part(b) step 1: given information

(b) Again because of the small element of charge dq, the small potential at P,

Hence, the potential at point P, due to the entire rod is given as

V = \int d V = \frac{2}{4 π x L} \int_{0}^{L} \frac{x}{d + x} d x = \frac{2 O}{4 π + L^{2}} \int_{0}^{L} (1 - \frac{d}{d + x}) d x = \frac{2 Q}{4 π \cdot} \{1 - \frac{d}{l} \ln (1 + \frac{L}{d})\}

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

A thin rod of length L and total charge Q has the nonuniform CALC linear charge distribution $λ (x) = λ_{0} x / L$ , where x is measured from the rod's left end.
a. What is $λ_{0}$ in terms of Q and L ?
b. What is the electric potential on the axis at distance d left of the rod's left end?

Step by Step Solution

Step 1: Given information

part(a) step 1: given information

part(b) step 1: given information

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

A thin rod of length L and total charge Q has the nonuniform CALC linear charge distribution λ(x)=λ0x/L, where x is measured from the rod's left end.a. What isλ0 in terms of Q and L ?b. What is the electric potential on the axis at distance d left of the rod's left end?

Step by Step Solution

Step 1: Given information

part(a) step 1: given information

part(b) step 1: given information

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

A thin rod of length L and total charge Q has the nonuniform CALC linear charge distribution $λ (x) = λ_{0} x / L$ , where x is measured from the rod's left end.
a. What is $λ_{0}$ in terms of Q and L ?
b. What is the electric potential on the axis at distance d left of the rod's left end?