A straight wire with radius a and magnetic permeability carries a conduction current density j 0

Question:

A straight wire with radius a and magnetic permeability μ carries a conduction current density j₀ = j₀ẑ = ẑ /0 πa².

(a) Find the induced magnetization M and the volume and surface magnetization current densities when the wire is exposed to a uniform external field B₀= B₀x̂.

(b) Show that the Lorentz force F = ∫ d³r j × B = I₀B₀ŷ, where j is the total current density and B is the total magnetic field.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Electrodynamics

ISBN: 9780521896979

1st Edition

Authors: Andrew Zangwill

See More Books

Question Posted: Aug 10, 2023 10:44 AM

See More Questions

A circular loop of radius R carries a current I 1 . A straight wire with a current I 2 in the plane of the loop passes a distance d from the loop center. (a) Use an energy method to show that the...
The motion of a charged particle in an electromagnetic field can be obtained from the Lorentz equation for the force on a particle in such a field, if the electric field vector is E and the magnetic...
(a) Starting from the force equation (5.12) and the fact that a magnetization M inside a volume V bounded by a surface S is equivalent to a volume current density J M = ( M) and a surface current...
Implement and maintain internal control procedures This task will require you to roleplay a meeting with your supervisor, Chris Kohler. You will discuss the reporting requirements and timetables...
Refer to the data for Lindex Company in Exercise 42. In Exercise 42, Lindex Company uses a process costing system. The following data are available for one department for October: The department...
The comparative statement of financial position for Charmaine Retailers Ltd. follows: Additional information: 1. Profit was $62,000 in 2015. 2. Depreciation expense was $21,000 in 2015. 3. Payments...
Estimate the work done by the force plotted in Figure P9.46 for an object displaced from $x=1.0 \mathrm{~m}$ to $x=3.0 \mathrm{~m}$. Data from Figure P9.46 F(N) 3 2 1 2 3 x (m) 4
Rocky Mountain Sounds Corp., an electric guitar retailer, was organized by Cathy Dewitt, Melody Leimbach, and Mario Torres. The charter authorized 250,000 shares of common stock with a par of $40....
Management - Mo through Z - questions Some of the questions suggested in the "RoughShould there be a set amount/limit that management will pay for new boots, jackets, and cold-weather gear?...
(a) A cylindrical solenoid occupies the interval L/2 z L/2, has radius R, and is wound tightly with N turns of a wire which carries current I. Use superposition and derive an expression for the...
A uniform external field B ext = B ext x is applied to an infinitely long cylindrical shell with inside radius a, outside radius b, and relative permeability m = / 0 . The rest of space is vacuum....
Refer to PengAtlas Map 2.4 (European Union) and note those EU members that use the euro. Note also PengAtlas Map 3.4 (Top 10 and Bottom 10 countries by GDP) and compare to Map 2.4. Which country that...
What is a dual-currency bond?
a. What is a Eurobond? b. How often is the coupon payment on a Eurobond made? c. Name the two currencies most often used to denominate Eurobonds.
Read the table below relating to Canada: Calculate the economic growth rate: a) from 2015 to 2016 b) from 2016 to 2017. Year 2015 2016 2017 Real GDP (millions of $] 1,697,000 1,721,000 1,774,000
Explain how federal funds are related to the reserve requirements that the Federal Reserve places on commercial banks.
What is the chief reason that the fed funds rate is an unusually volatile short-term interest rate?
Claim: three-fourths of all adults believe that it is important to be involved in their communities. Based on a USA Today/Gallup poll of 1021 randomly selected adults, 89% believe that it is...
F.(3e* -2x 3 sin(2x)) is equal to 2 3 Cos 8. IT 3, t (4+@ 2 3, 1+o 1 4 Cos 4 4 1 3. 1 +4cos V7 (1+o 4 1 4 Cos 4 1+0 4-
The parabolic plate is subjected to a fluid pressure that varies linearly from 0 at its top to 100 lb>ft at its bottom B. Determine the magnitude of the resultant force and its location on the plate....
The tank is used to store a liquid having a density of 80 lb/ft 3 . If it is filled to the top, determine the magnitude of force the liquid exerts on each of its two sides ABDC and BDFE. D 4 ft B 6...
A wind loading creates a positive pressure on one side of the chimney and a negative (suction) pressure on the other side, as shown. If this pressure loading acts uniformly along the chimneys length,...
Develop an IT innovation strategy for your organization (or an organization you are familiar with). Describe the organization's situation and how a specific innovation approach (disruptive,...
The current gain of a BJT operating at a collector current of 16.8 mA is 200. Calculate its input resistance. Give your answer in k and round it to three decimal places.
The following were taken from the books of Satellite Company. January 1 P 335,000 March 31 P 208,750 Raw materials Work in process Finished goods Direct materials used Direct labor Factory overhead...

A straight wire with radius a and magnetic permeability carries a conduction current density j 0

Question:

Step by Step Answer:

a b B o H M H so M o1H We find H from V x H jo Ampres law gives the particular solu...View the full answer

Modern Electrodynamics

Students also viewed these Engineering questions