Show that the flux of (mathbf{F}=frac{mathbf{e}_{r}}{r^{2}}) through a sphere centered at the origin does not depend on

Question:

Show that the flux of $\mathbf{F}=\frac{\mathbf{e}_{r}}{r^{2}}$ through a sphere centered at the origin does not depend on the radius of the sphere.

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

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 24, 2024 08:01 AM

See More Questions

The bond price is $1174, given the semiannual payment, coupon rate of 5%, and maturity of 30 years and required rate of return of 4%. If the interest rate increase, and thus, the required rate of...
The hydrogen atom is composed of one proton in the nucleus and one electron, which moves about the nucleus. In the quantum theory of atomic structure, it is assumed that the electron does not move in...
A point charge q is located at the center of a uniform ring having linear charge density A and radius a, as shown in Figure P24.6. Determine the total electric flux through a sphere centered at the...
i. Find a. b. ii. Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. +6 e2x + 6 e2 dx,
A source of light is located at a distance l = 90 cm from a screen, A thin converging lens provides the sharp image of the source when placed between the source of light and the screen at two...
Why do marketers like Apple find it important to embrace societal needs and ethical business practices? Provide an example of a societal need or ethical business practice that Apple is addressing.
Refer to the information in Exercise 24-3 and assume instead that double-declining depreciation is applied. Compute the machines payback period (ignore taxes). (Round the payback period to three...
Workplace Products Inc., a wholesaler of office products, was organized on February 1 of the current year, with an authorization of 10,000 shares of preferred 2% stock, $120 par and 250,000 shares of...
The force exerted by a 2.4-m massless string on a 0.84-kg object being swung in a horizontal circle is 4.2 N. What is the tangential velocity of the object?
The electric field due to a point charge located at the origin in $\mathbf{R}^{3}$ is $\mathbf{E}=k \frac{\mathbf{e}_{r}}{r^{2}}$, where $r=\sqrt{x^{2}+y^{2}+z^{2}}$ and $k$ is a constant....
Let $\mathbf{e}_{\mathbf{r}}=\langle x / r, y / r, z / rangle$ be the unit radial vector, where $r=\sqrt{x^{2}+y^{2}+z^{2}}$. Calculate the integral of $\mathbf{F}=$ \(e^{-r}...
During the 2008-2009 financial crisis, the stock market plummeted, and many companies tried to take advantage of the depressed prices by buying back large amounts of their own stock. Amazon, for...
For a project manager working in the federal government, creating an Independent Government Cost Estimate (IGCE) is crucial to defining and developing successful acquisitions. What is the primary...
Best Poor Man's Country and Revolution What were the opportunities for individuals in this time period, share with the class the insights that you perceived about Pennsylvania? Did everyone have an...
You are right about any policy starting up needing a funding source. Determining where that funding will come from can be the hard part. It is important to map out a budget for the policy and promote...
What characteristics of a commonweal organization would likely conflict with the culture of a typical business organization that contracts to provide a public service?
1. Why did Mexicans volunteer for service during World War II? 2. What role did Mexican women play in the home front during the war? 3. What impact did urban living have on Mexicans? 4. Who were the...
Go to this texts Web site at academic. cengage.com/blaw/clarkson and select Chapter 49. Click on Video Questions and view the video titled Double Indemnity. Then answer the following questions. (a)...
(8%) Problem 6: A student attaches a f= 3.5 kHz oscillator to one end of a metal rail of length L = 25 m. The student turns on the oscillator and uses a piezoelectric gauge at the other end to...
Use a table of integrals to evaluate the following integrals. dx xV4x 6 X
Use a table of integrals to evaluate the following integrals. 7/2 do 1 + sin 20
Use a table of integrals to evaluate the following integrals. sec 5 x dx
illustrate the distribution channels for the NEW indirect sales methods. Indicate the PRICE that each channel member will pay for ONE container for protein. Also include the price for the final...
Set up and evaluate expressions to solve the following map problems. 1 (a) Each inch on a map represents an actual distance of 4 miles. If the map shows town A as being 7 inches due east of town B,...
Let R stand for radiation exposure, t stand for length of time of exposure, r stand for distance, and k be the constant of variation. Write an equation of joint variation representing the...

Show that the flux of (mathbf{F}=frac{mathbf{e}_{r}}{r^{2}}) through a sphere centered at the origin does not depend on

Question:

Step by Step Answer:

We parametrize the sphere of radius R centered at the origin by Phi xR cos t...View the full answer

Calculus

Students also viewed these Mathematics questions