Using Eq. 5.86, calculate the average magnetic field of a dipole over a sphere of radius R
Question:
Using Eq. 5.86, calculate the average magnetic field of a dipole over a sphere of radius R centered at the origin. Do the angular integrals first. Compare your answer with the general theorem in Prob. 5.57. Explain the discrepancy, and indicate how Eq. 5.87 can be corrected to resolve the ambiguity at r = 0. (If you get stuck, refer to Prob. 3.42.) Evidently the true field of a magnetic dipole is compare the electrostatic analog, Eq.3.106.
2μ40. 3 HO 1 Bdip(r): 47 73 [3(m-f)r-m] + - m8³ (r). (5.90)
Step by Step Answer:
The issue and the integral is identical to the one in Prob 342 The resolution ...View the full answer
Related Video
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. The video shows the practical implications of magnetic force around different objects.
Students also viewed these Electrodynamics questions
-
In 1962, measurements of the magnetic field of a large tornado were made at the Geophysical Observatory in Tulsa, Oklahoma. If the magnitude of the tornados field was B = 1.50 x 108 T pointing north...
-
Show that the stator magnetic field of a three-phase generator has a constant magnitude and rotates with constant angular frequency. You can assume that the magnetic fields produced by the stator...
-
2 [ * + = { sin cosm (m-1)!!(n-1)!! (m+n)!! (m-1)!!(n-1)!! (m+n)!! m, n both even any other case
-
You recently joined an accounting consulting firm. Your first client is a new manufacturing start-up that is trying to set up their costing system, and develop good processes for their upcoming...
-
Why is there only one U.S. bank among the ten largest banks in the world?
-
The following information was taken from Lamberson Companys accounting records: Additional information for the year: a. b. Dividends declared and paid totaled $700. c. On January 1,2016, convertible...
-
The figure below shows the results of a survey in which 1000 adults were asked how much they spend in preparation for personal travel each year. Make a frequency distribution for the data. Then use...
-
A company retired $60 million of its 6% bonds at 102 ($61.2 million) before their scheduled maturity. At the time, the bonds had a remaining discount of $2 million. Prepare the journal entry to...
-
The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the...
-
Stockholders equity totaled $246,000 at the beginning of the year. During the year, net income was $36,000, dividends of $9,000 were declared and paid, and $30,000 of common stock was issued at par...
-
A uniformly charged solid sphere of radius R carries a total charge Q, and is set spinning with angular velocity co about the z axis. (a) What is the magnetic dipole moment of the sphere? (b) Find...
-
I worked out the multipole expansion for the vector potential of a line current because that's the most common type, and in some respects the easiest to handle. For a volume current J: (a) Write down...
-
The Springfield Family Community Center has an outdoor pool that operates May through October. The director is interested to learn if the Community Center can afford the $57,000 cost to install a...
-
Let \(a\) and \(\sigma\) be continuous deterministic functions, \(B\) a BM and \(X\) the solution of \(d X_{t}=a(t) X_{t} d t+\sigma(t) d B_{t}, X_{0}=x\). Let \(T_{0}=\inf \left\{t \geq 0, X_{t}...
-
Let \(H\) be a measurable map defined on \(\mathbb{R}^{+} \times \Omega \times \mathbb{R}\). Prove that, for any random time \(\tau\), \[\int_{0}^{\tau} H\left(s, \omega, B_{s} ight) d...
-
Indicate whether each of the following statements is true or false by writing T or F in the answer c olumn. The writing a holder puts on the back of a negotiable instrument is known as a negotiation.
-
If the governments budget is a deficit of $1 trillion, what are the real interest rate and investment? Does any crowding out occur? Problem 8 The table sets out the data for an economy when the...
-
Let \(B\) be a \(d\)-dimensional Brownian motion, with \(d \geq 2\) and \(\beta\) defined as \[d \beta_{t}=\frac{1}{\left\|B_{t} ight\|} B_{t} \cdot d B_{t}=\frac{1}{\left\|B_{t} ight\|}...
-
A converging lens creates a real, inverted image. For this to occur, the object must be A. Closer to the lens than the focal point. B. Farther from the lens than the focal point. C. At the focal...
-
Show that every group G with identity e and such that x * x = e for all x G is abelian.
-
In 2009, Elegant Beverages, LLC, and Imperial Unlimited Services, Inc., were two beverage businesses that were sold to Mark Gandino from Thomas, Kathleen, and Loudine Dotli. The beverage companies...
-
A tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.20 atm?
-
An auditorium has dimensions 10.0 m X 20.0 m X 30.0 m. How many molecules of air fill the auditorium at 20.0C and a pressure of 101 kPa?
-
Imagine a baby alien playing with a spherical balloon the size of the Earth in the outer solar system. Helium gas inside the balloon has a uniform temperature of 50.0 K due to radiation from the Sun....
-
What is the minimum quantity firms need to sell in order to start earning profit given insurance costs of $50,000, materials o per unit, and break even quantity is 1500?
-
Assume a 10% discount rate and compute the present value of Rs. 1100, Rs.900, Rs.1500 andRs.700 received at the end of 1-4 years In the above sum if the amounts are received at the beginning of the...
-
Recall that an FX rate XXXYYY = Bid/Offer gives the rate of YYY per XXX. You can buy XXX/sell YYY at the offer price and sell XXX/buy YYY at the bid price. EURUSD is trading at 1.4760/1.4763 USDJPY...
Study smarter with the SolutionInn App