University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 12, Problem 53P
Determine the magnetic field on the central axis at the opening of a semi-infinite solenoid. (That is, take the opening to be at x = 0 and the other end to be at
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
There is a long cylinder with radius of R, and magnetization of M = Mopî for p
A uniform magnetic field B has constant strength b in the z-direction [i.e., B = (0, 0, b)]. Verify that A= ½B x r is a vector potential for B, where r = (x, y, 0).
Determine the magnetic field on the central axis at the opening of a semi-infinite solenoid. (That is, take the opening to be at x = 0 and the other end to be at x = ∞. )
Chapter 12 Solutions
University Physics Volume 2
Ch. 12 - Check Your Understanding Using Example 12.1, at...Ch. 12 - Check Your Understanding The wire loop forms a...Ch. 12 - 12.3 Check Your Understanding Using Example 12.3,...Ch. 12 - 12.4 Check Your Understanding Two wires, both...Ch. 12 - Check Your Understanding Using Example 12.5, at...Ch. 12 - Check Your Understanding Consider using Ampere’s...Ch. 12 - 12.7 Check Your Understanding What is the ratio of...Ch. 12 - Check your Understanding Repeat the calculations...Ch. 12 - For calculating magnetic fields, what are the...Ch. 12 - Describe the magnetic field due to the current in...
Ch. 12 - How can you decide if a wire is infinite?Ch. 12 - Identical currents are carried in two circular...Ch. 12 - How would you orient two long, straight, current...Ch. 12 - Compare and contrast the electric field of an...Ch. 12 - Is B constant in magnitude for points that lie on...Ch. 12 - Is the magnetic field of a current loop uniform?Ch. 12 - What happens to the length of a suspended spring...Ch. 12 - Two concentric circular wines with different...Ch. 12 - Is Ampere’s law valid for all closed paths? Why...Ch. 12 - Is the magnetic field inside a toroid completely...Ch. 12 - Explain why B=0 inside a long, hollow copper pipe...Ch. 12 - A diamagnetic material is brought dose to a...Ch. 12 - If you cut a bar magnet into two pieces, will you...Ch. 12 - A 10-A current flows through the wire shown. What...Ch. 12 - Ten amps flow through a square loop where each...Ch. 12 - What is the magnetic field at P due to the current...Ch. 12 - The accompanying figure shows a current loop...Ch. 12 - Find the magnetic field at the center C of the...Ch. 12 - Two long wires, one of which has a semicircular...Ch. 12 - A typical currant in a lightning bolt is 104 A....Ch. 12 - The magnitude of the magnetic field 50 cm from a...Ch. 12 - A transmission line strung 7.0 m above the ground...Ch. 12 - A long, straight, horizontal wire carries a...Ch. 12 - The two long, parallel wires shown in the...Ch. 12 - The accompanying figure shows two long, straight,...Ch. 12 - Repeat the calculations of the preceding problem...Ch. 12 - Consider the area between the wires of the...Ch. 12 - Two long, straight wires are parallel and 25 cm...Ch. 12 - Two long, straight wires are parallel and 10 cm...Ch. 12 - Two long, parallel wires are hung by cords of...Ch. 12 - A circuit with current I has two long parallel...Ch. 12 - The infinite, straight wire shown in the...Ch. 12 - When the current through a circular loop is 6.0 A,...Ch. 12 - How many turns must be wound on a flat, circular...Ch. 12 - A flat, circular loop has 20 turns. The radius of...Ch. 12 - A circular loop of radius R carries a current I....Ch. 12 - Two flat, circular coils, each with a radius R and...Ch. 12 - For the coils in the preceding problem, what is...Ch. 12 - A current 1 flows around the rectangular loop...Ch. 12 - Evaluate BdI for each of the cases shown in the...Ch. 12 - The coil whose lengthwise cross section is shown...Ch. 12 - A superconducting wire of diameter 0.25 cm carries...Ch. 12 - A long, straight wire of radius R caries a current...Ch. 12 - The accompanying figure shows a cross-section of a...Ch. 12 - A long, solid, cylindrical conductor of radius 3.0...Ch. 12 - A portion of a long, cylindrical coaxial cable is...Ch. 12 - A solenoid is wound with 2000 turns pet meter....Ch. 12 - A solenoid has 12 turns per centimeter. What...Ch. 12 - If a current is 2.0 A, bow many turns per...Ch. 12 - A solenoid is 40 cm long, has a diameter of 3.0...Ch. 12 - Determine the magnetic field on the central axis...Ch. 12 - By how much is the approximation B=0nI in error at...Ch. 12 - A solenoid with 25 turns per centimeter carries a...Ch. 12 - A toroid has 250 trims of wire and carries a...Ch. 12 - A toroid with a square cross section 3.0cm3.0cm...Ch. 12 - The magnetic field in the core of an air-filled...Ch. 12 - A solenoid has a ferromagnetic core, n = 1000...Ch. 12 - A 20-A current flows through a solenoid with 2000...Ch. 12 - The magnetic dipole moment of the iron atom is...Ch. 12 - Suppose you wish to produce 1.2-T magnetic field...Ch. 12 - A current of 1.5 A flows through the windings of a...Ch. 12 - A solenoid with an iron core is 25 cm long and is...Ch. 12 - Three long, straight, parallel wires, all carrying...Ch. 12 - A current I flows around a wire bent into the...Ch. 12 - The accompanying figure shows a long, straight...Ch. 12 - Current flows along a thin, infinite sheet as...Ch. 12 - (a) Use the result of the previous problem to...Ch. 12 - We often assume that the magnetic field is uniform...Ch. 12 - How is the percentage change in the strength of...Ch. 12 - Show that the expression for the magnetic field of...Ch. 12 - A toroid with an inner radius of 20 cm and an...Ch. 12 - A wire element has dI,IdI=JAdl=Jdv , where A and...Ch. 12 - A reasonably uniform magnetic field over a limited...Ch. 12 - A charge of 4.0C .s distributed uniformly around a...Ch. 12 - A thin, nonconducting disk of radius R is free to...Ch. 12 - Consider the disk in the previous problem....Ch. 12 - Consider the axial magnetic field...Ch. 12 - The current density in the long, cylindrical wire...Ch. 12 - A long, straight, cylindrical conductor contains a...Ch. 12 - Between the two ends of a horseshoe magnet the...Ch. 12 - Show that the magnetic field of a thin wire and...Ch. 12 - An Ampere loop is chosen as shown by dashed lines...Ch. 12 - , A ray long, thick, cylindrical wire of radius R...Ch. 12 - A very long, cylindrical wire of radius a has a...Ch. 12 - Magnetic field inside a torus. Consider a torus of...Ch. 12 - Two long coaxial copper tubes, each of length L,...Ch. 12 - The accompanying figure shows a flat, infinitely...Ch. 12 - A hypothetical current flowing in the z-direction...Ch. 12 - A nonconducting hard rubber circular disk of...
Additional Science Textbook Solutions
Find more solutions based on key concepts
Two point charges exert a 5.00 N force on each other. What will the force become if the distance between them i...
College Physics
19. What is the relationship between work and power?
Conceptual Physical Science (6th Edition)
The force, when you push against a wall with your fingers, they bend.
Conceptual Physics (12th Edition)
Youre working on the script of a movie whose plot involves a hole drilled straight through Earths center and ou...
Essential University Physics (3rd Edition)
Choose the best answer to each of the following. Explain your reasoning. Did a large terrestrial planet ever fo...
The Cosmic Perspective Fundamentals (2nd Edition)
20.(I) A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley an...
Physics: Principles with Applications
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
- (a) Calculate the vector potential of two straight, infinitely long wires carrying steady antiparallel currents I. Using the vector potential, calculate the magnetic field B at any point P. What is B along the line midway between the two wires? (b) Do the same for the case of parallel currents.arrow_forwardFind the potential vector A at a distance of 7 cm from the axis of an infinitely long solenoid with a radius of 2 cm with a magnetic field of 0,3 T.arrow_forwardIn cylindrical coordinates (p, o, z), the vector potential A 0 = Hol O = - OB= 2mp OB=W = 2″ Pat a point p distance from the z axis. Find the corresponding magnetic field Barrow_forward
- Question 5.8: A closely wound solenoid of 2000 turns and area of cross-section 1.6 x 10- m2, carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane. (a) What is the magnetic moment associated with the solenoid?arrow_forwardThe magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let p = (x² + y² + z²)¹/² For p large, B = curl(A), where A = (-33, -3,0) R Current loop (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Which of the following correctly explains why A is tangent to C? A(c(t)) = So, A(c(t)) = A(c(t)) -(-² A(c(t)) = = A(c(t)) cos(0,0) p3 (1). Therefore, A is parallel to c'(t) and tangent to C. Rcos(t) R sin(t) = (-OS R sin(t) R cos(1) p³ So, A(c(1)) = -c'(1). Therefore, A is parallel to c'(t) and tangent to C. O BdS = = and c'(t)= (-R sin(t), R cos(t), 0) Rin(1,0) and c'(t) = (R cos(1), -R sin(1), 0) So, A(c(t)) c(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C. O R sin(1) R cos(1) (R$ R COS(0,0) and c'(t) = (R cos(t), - R sin(t), 0) R cos(1) p3 So, A(c(t)) - c'(t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. R sin(t) - and c'(t)= (-R sin(t), R…arrow_forwardConsider two infinitely long and parallel wires separated by distance d and carrying currents I₁ = -12. (a) Find the magnitude and direction of the vector potential A(r1,72) at a point P where r₁ and r2 represent the distances to P from wire 1 and wire 2 respectively. (b) What is the magnitude of A for r₁ = r₂? (c) What is the value of the magnetic field B for r₁ = r₂? (d) Given that B = V x A, how can you reconcile the answers to (b) and (c) above?arrow_forward
- Consider a solenoid of length L and radius R, where R«L. A steady-current flows through the solenoid. The magnetic field is uniform inside the solenoid and zero outside. L/2 L Among the given options, choose the one that best represents the variation in the magnitude of the vector potential, (0,A,,0) at z=L/2, as a function of the radial distance (r) in cylindrical coordinates. Useful information: The curl of a vector F, in cylindrical coordinates is [a(rF,) &F, or 1a VXF(r,o.z) = f r ôp 14, (a) (b) R R A, 14, (c) (p) Rarrow_forwardIf A and B are irrotational, prove that A x B is Solenoidal that is div (A x B) =arrow_forwardA uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b) ] (a) Verify that A = Bxr is a vector potential for B, where r = (x, y, 0) (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. A Flux(B) = = D B FIGURE 17 A = (8,0,1), B = (8,5, 0), C = (0,5, 0), D = (0, 0, 1), F = (8,0,0)arrow_forward
- Consider two long parallel wires each carrying a current I and in the same direction as the z-axis. The wires cross the xy-plane at x = (a, 0) and at x =( -a, 0) . Calculate the magnetic field at a point (x,y,0) in the xy plane .One wire is at x = - a and theother at x = + a (both parallel to z-axis.)arrow_forwardCalculate the magnetic field and vector magnetic potential on axis resulting form z-directed magnetic dipole located at z=z0arrow_forwardConsider a toroid consisting of N turns of a single wire with current I flowing through it. Compute the magnitude of the magnetic field as a function of r inside the toroid, that is, inside of the wire loops where there is field.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Magnets and Magnetic Fields; Author: Professor Dave explains;https://www.youtube.com/watch?v=IgtIdttfGVw;License: Standard YouTube License, CC-BY