Question: Prove the following uniqueness theorem: If the current density J is specified throughout a volume V, and either the potential A or the magnetic field

Prove the following uniqueness theorem: If the current density J is specified throughout a volume V, and either the potential A or the magnetic field B is specified on the surface $ bounding V, then the magnetic field itself is uniquely determined throughout V.

f100x1 {(V x U). (V x V)-U. [V x (V x V)]}

f100x1 {(V x U). (V x V)-U. [V x (V x V)]} dt = f[u (V \ (V x V)] da,

Step by Step Solution

★★★★★

3.35 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Apply the divergence theorem to the function U V x V noting f... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

5-P-E-M (52).docx

120 KBs Word File

Students Have Also Explored These Related Electrodynamics Questions!

Prove the following uniqueness theorem: A volume 1; contains a specified free charge distribution, and various pieces of linear dielectric material, with the susceptibility of each one given. If the...

Prove Theorem 1.4. Assume that V and W are vector spaces of dimensions n and m with bases B and D, and that h: V W is a linear map. If h is represented by and V is represented by then the...

A uniform magnetic field B has constant strength b in the z-direction [that is, B = (0, 0, b)]. (a) Verify that A = 12 B Ã r is a vector potential for B, where r = (x, y, 0). (b) Calculate the...

Prove the following uniqueness theorem: A volume V contains a specified free charge distribution, and various pieces of linear dielectric material, with the susceptibility of each one given. If the...

E-Physics Tutorial Book Note: I have attached below the lesson for the 3 activities. Thank you so much for your time and effort. Activity 1. Directions: Use the right-hand rule to determine the...

) Why is the mass of the earth important to maintain life as we know it? A) If the earth's mass were significantly different, we would be bombarded by cosmic rays that would strip away our...

Question Two Read the fact pattern below and answer the following questions in paragraph format. Fahad had a student loan that was in arrears. Collection of the loan had been transferred from the...

Supply Chain Management Introduction Outline What is supply chain management? Significance of supply chain management. Push vs. Pull processes utdallas.edu/~metin 1 A Generic Supply Chain Sources:...

Riley Fontaine has requested that you review the calculation of his 20X1 net income for tax purposes. He has provided you with the following information: 1. His salary consists of the following: The...

Carry out an orbital symmetry analysis to show that suprafacial [1,5] carbon migrations should occur with retention of configuration in the migrating group.

The bid price is the: Multiple Choice 0 . 3 9 2 0 price you must charge to break even at a rero discount rate. afertas contribuhtion margin. highest price you should charge if you want to win the...

The cost of direct materials cannot easily be traced to the manufactured product, and therefore, it is a component of manufacturing overhead. True or False

In 2010, the Government of Mauritius launched, with UNDP support, the Small-Scale Distributed Generation (SSDG) scheme, which has assisted 237 households, schools and public institutions to install...

the duration she estimated for each task: First, you need to meet with all farm staff that support all aspects of the business including a horticulturist who is a likely first inclusion in the...

The Bristol Port Company (BPC) was formed in 1991 when entrepreneurs Terence Mordaunt and David Ord purchased the Port of Bristol from Bristol City Council. Since privatisation over 500 million has...

Plaintiff Caruso was gambling at the Foxwoods Casino, which was owned by defendant Mashantucket Pequot Gaming Enterprise. When he went to use the restroom, Caruso noticed an attendant holding a mop...

The active element of a certain laser is made of a glass rod 30.0 cm long by 1.50 cm in diameter. If the temperature of the rod increases by 65.0C, what is the increase in (a) Its length, (b) Its...

Inside the wall of a house, an L-shaped section of hot-water pipe consists of a straight horizontal piece 28.0 cm long, an elbow, and a straight vertical piece 134 cm long (Figure P19.14). A stud and...

A brass ring of diameter 10.00 cm at 20.0C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0C. Assuming the average coefficients of linear expansion are constant, (a) To what...

At the beginning of the month, the Forming Department of Martin Manufacturing had 22,000 units in inventory, 30% complete as to materials, and 10% complete as to conversion. During the month the...

Cash fow to the waman under an interest-only loan, in which Poryi will pay the annual intecest expense each year and pay the principal back at the end of the contract What is the amount of payment...

A project will produce operating cash flows of $45,000 a year for four years. During the life of the project, inventory will be lowered by $30,000 and accounts receivable will increase by $15,000....