ProblemAn electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius Rand length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Considerthe cases inside and outside the wire)SolutionTo find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed asWe will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, thenevaluate the dot product to obtainA =(Equation 1)Case 1: Inside the wireSince, r falls inside the wire, then all the enclosed charge must be:dencOn the other hand, the Gaussian surface inside the wire is given byA =Using Equation 1, the electric field in simplified form isE = Case 2: Outside the wireSince, r falls outside the wire, then, all the charge must be enclosed, thusdenc%3DOn the other hand, the Gaussian surface outside the wire is given byA =Using Equation 1, the electric field in simplified form isE =

According to Gauss' law total electric flux through or coming out of a closed surface is equal to…

An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire)

An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire)

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)...

See similar textbooks

Related questions

Q: Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an…

A: The formula for electric field due to first disk is E1 = k [ 1 - z / √( z 2 + R 2 ) =k [ 1 -…

Q: C

Q: A small object of mass 3.78 g and charge −17.8 ?C is suspended motionless above the ground when…

Q: The electric field at point P is 5.9 x 1020 N/C @ 241o. What is the angle of the force experienced…

A: Given data The electric field is E=5.9×1020 N/C The angle of the electric field is θ=241o The charge…

Q: An electron initially at rest is released in a uniform electric field, and the electron is…

Q: For a charged conductor in electrostatic equilibrium, the electric field just outside the surface of…

A: Given in question - For a charged conductor in electrostatic equilibrium, the electric field just…

Q: A proton and an electron are moving due east in a constant electric field that also points due east.…

A: Magnitude of electric field, E= 7.0 x 104 N/C

Q: A small object of mass 3.60 g and charge −18.5 ?C is suspended motionless above the ground when…

Q: Would be able to help me answer this please? Consider a straight, non-conducting rod of length L…

A: Given data- total length of rod = L charge density is increasing linearly with distance i.e.…

Q: A small object with mass mm, charge qq, and initial speedv0v0 = 6.00×103 m/sm/s is projected into a…

A: charge = q Mass = m E = 800 NCvo = 6000 m/s d = 1.15 cm = 0.0115 m L = 26 cm = 0.26 m D = 26 + 56 cm…

Q: Earth has an electric charge of approximately −5.7×105C distributed relatively uniformly on its…

Q: In a certain region of space, the electric field is E with arrow = 5.09 103 x2 î, where E with arrow…

Q: A uniform electric field of magnitude E = 22 N/C points along the x-axis. A circular loop of radius…

Q: An electron with charge e travelling at a horizontal speed of 1.50 x 10 m s¹ enters a region of…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If the total charge on a uniformly charged rod of length 0.7 m is 8.6 nC, what is the magnitude of…

A: Length of the rod is L = 0.7 m Charge on the rod is q = 8.6 nC

Q: The electric field in a certain region of Earth's atmosphere is directed vertically down. At an…

A: Given, The electric field in a certain region of Earth's atmosphere is directed vertically down. At…

Q: nd the electric field dE at a point xo (where xo is a positive number) on the positive x-axis due to…

Q: A closed surface is constructed in the space between two large parallel metal plates, where there is…

A: Magnitude of electric field,Area increment ,Then,The electric flow through any surface is denoted…

Q: An electron is released from rest in a uniform electric field. The electron accelerates vertically…

Q: A small object of mass 4.12 g and charge −19.4 μC is suspended motionless above the ground when…

Q: An electric field in a region of space is directed 45° north of west. A proton is placed in this…

A: Electric field E is pointing 45o north of west.

Q: It is found experimentally that the electric field in a certain region of Earth's atmosphere is…

A: This question is based on Gauss law.

Q: 21. An ideal spring with k = 6 N/m is initially compressed 0.40 m. One end is attached to a wall and…

Q: uniform electric field of magnitude E = 38 N/C points along the x-axis. A circular loop of radius R…

Q: Find the electric field at P in the figure shown below. (Take r = 1.2 m and 0 = 38°. Measure the…

A: We know that the here We have given the two charg of equal value of q and the point P is from the…

Q: A ring-shaped conductor with radius a = 2.30 cm has a total positive charge Q = 0.121 nC uniformly…

A: According to Coulomb's law, force between any two charges separated by a fix distance is directly…

Q: An insulating sphere of radius R has a non-uniform charge density given byp = Ar 2 for r R. Find…

A: To determine: What is the electric field inside and outside the sphere of an insulating sphere?

Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

Problem
An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R
and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider
the cases inside and outside the wire)
Solution
To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as
We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then
evaluate the dot product to obtain
A =
(Equation 1)
Case 1: Inside the wire
Since, r falls inside the wire, then all the enclosed charge must be:
denc
On the other hand, the Gaussian surface inside the wire is given by
A =
Using Equation 1, the electric field in simplified form is
E =

Case 2: Outside the wire
Since, r falls outside the wire, then, all the charge must be enclosed, thus
denc
%3D
On the other hand, the Gaussian surface outside the wire is given by
A =
Using Equation 1, the electric field in simplified form is
E =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1 Write down Gauss' Law

VIEW

Step 2 Calculate Electric Field inside the conducting wire by considering a surface of radius r<R

VIEW

Step 3 Calculate Electric field outside the conducting wire but taking a surface of radius r>R

VIEW

Step 4 Conclusion

VIEW

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

In this example, we will analyze the motion of an electron that is released in an electric field. The terminals of a 100 V battery are connected to two large, parallel, horizontal plates 1.0 cm apart. The resulting charges on the plates produce an electric field E in the region between the plates that is very nearly uniform and has magnitude E = 3.0×104 N/C. Suppose the lower plate has positive charge, so that the electric field is vertically upward, as shown in (Figure 1). (The thin pink arrows represent the electric field.) If an electron is released from rest at the upper plate, what is its speed just before it reaches the lower plate? How much time is required for it to reach the lower plate? The mass of an electron is mẹ = 9.11 x 10-31 kg. The thin arrows represent the uniform electric field. 1.0 cm 100 V In this example, suppose a proton (mp = 1.67 × 10-27 kg) is released from rest at the positive plate. What is its speed just before it reaches the negative plate? Express your…
The electric field at point P is 9.3 x 1020 N/C @ 343°. What is the angle of the force experienced by a proton if it is placed at point P. Express your answer in degrees.
A long, straight metal rod has a radius of 4.00 cm and a charge per unit length of 31.6 nC/m. Find the electric field at the following distances from the axis of the rod, where distances are measured perpendicular to the rod's axis.
A proton and an electron are moving due east in a constant electric field that also points due east. The electric field has a magnitude of 2.0 × 104 N/C. Determine the magnitude of the acceleration of the proton and the electron.
A square window of side length d lies in the y-z plane. The electric field everywhere in the area of the window is given by = ai + bj+ ck , where a = 4.00 N/C, b = 8.00 N/C, and c = 15.0 N/C. (a.) Which of the following area vectors describes the area and orientation of the window? (b.) Let the side length of the window be d = 20.0 cm = 0.200 m. What is the electric flux through the window, in Nm2/C?
A small object of mass 3.54 g and charge −19.3 ?C is suspended motionless above the ground when immersed in a uniform electric field perpendicular to the ground. What are the magnitude and direction of the electric field? magnitude direction
Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 2.60R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/2.60 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P? Number i Units (a) (b)