Question: (a) A flux density field is given as F 1 = 5a z . Evaluate the outward flux of F 1 through the hemispherical surface,

(a) A flux density field is given as F₁ = 5a_z. Evaluate the outward flux of F₁ through the hemispherical surface, r = a, 0 < θ < π/2, 0 < ϕ < 2π.

(b) What simple observation would have saved a lot of work in part a?

(c) Now suppose the field is given by F₂ = 5za_z. Using the appropriate surface integrals, evaluate the net outward flux of F₂ through the closed surface consisting of the hemisphere of part a and its circular base in the x_y plane.

(d) Repeat part c by using the divergence theorem and an appropriate volume integral.

Step by Step Solution

★★★★★

3.43 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The flux integral is b The field is constant and so the inw... 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

Students Have Also Explored These Related Principles Communications Systems Questions!

Define health economics and differentiate it from related concepts such as health financing and reimbursement.

A field is given as G = [25/(x 2 + y 2 )](xa x + ya y ). Find (a) A unit vector in the direction of G at P(3, 4,2); (b) The angle between G and ax at P; (c) The value of the following double integral...

Given the electric flux density determine (a) pv by applying Eq. (4.26), (b) The total charge Q enclosed in a cube 2 m on a side, located in the first octant with three of its sides coincident with...

Consider the magnetic circuit of Figure. This structure, known as a pot-core, is typically made in two halves. The N-turn coil is wound on a cylindrical bobbin and can be easily inserted over the...

3. A greenhouse has a glass dome in the shape of the paraboloid z=82x22 and a flat wooden floor at z = 0. Let S be the closed surface formed by the dome and the floor, oriented with outward unit...

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...

solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks. 1. [-/1 Points] DETAILS SCALCET9 16.7.003. MY NOTES ASK YOUR TEACHER...

give me just answers of these questions. VA Topic 9 - HW 3: (Surface Integrals X VA Topic 9 - HW 4: (Stokes' Theorem X + X webassign.net/web/Student/Assignment-Responses/last?dep=24613344 . .. 3....

13. 14. 15. 16. 17. 18. A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y= 5 m. Which of the following integrals is correct for the magnitude (in WC) of...

1. [-/0.5 Points] DETAILS MY NOTES PRACTICE ANOTHER Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u - V, Z= 1+ 2u + v, Osus 3, OS VS...

1. [-/0.5 Points] DETAILS LARCALC11 15.8.007. Use Stokes's Theorem to evaluate F . dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with...

The banking sector is a major source of debt finance for most companies in Ghana. The Bank of Ghana in 2017 embarked on a major financial sector clean-up in an attempt to build a more robust...

A certain material occupies the space between two conducting slabs located at y = 2 cm. When heated, the material emits electrons such that v = 50(1 y2) C/m3. If the slabs are both held at 30 kV,...

2. Write assembly language instructions that calculate EAX * 21 using binary multiplication.

The preschool child sleeps approximately 10 to 12 hours per day. Daytime napping decreases or ceases, unless cultural norms dicate otherwise. Night sleep is often filled with vivid dreams and...

A second-order Butter worth filter has 3-dB bandwidth of 500 Hz. Determine the unit impulse response of the filter and use it to compute the noise-equivalent bandwidth of the filter. Check your...

The input to a low pass filter with impulse response h(t) = exp (-10t) u(t) is white, Gaussian noise with single-sided power spectral density of 2 W/Hz. Obtain the following: (a) The mean of the...

Obtain the auto correlation functions and power spectral densities of the outputs of the following systems with the input auto correlation functions or power spectral densities given. (a) Transfer...

Question 9 5 pts St. Thomas University (STU) plans to build an addition to the Gus Machado School of Business 4 years from today. It will need to have $8 million in an account at that time. It would...

Your firm is considering two one-year loan options for a $462,000 loan. The first carries fees of 2% of the loan amount and charges interest of 4.3% of the loan amount. The other carries fees of 1.6%...

For this question, may i ask why is the inclusion exclusion property required. Why can't I just take P(A can flow to B)= P(A1,A2) + P(A1,A3,A4) since water can flow through from A to B if either 1,2...