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Calculate the average over all directions of T: ((7.a) 7), where a is a fixed vector...
7. Calculate the divergence over the volume of a sphere of radius 3 in a vector field where =4rsin- cos.(r, with Deduce the flux through the surface of the sphere.
7. Calculate the divergence over the volume of a sphere of radius 3 in a vector field where =4rsin- cos.(r, with Deduce the flux through the surface of the sphere.
515P) Calculate (r is the usual position vector): 7:7, 7(r-), r •7(r) integrate this over a spherical volume radius b centered at origin: convert this to surface and volume integral.
Calculate (r is the usual position vector: (cose/r?), 7(rr), Yx(FxB) where B is constant vector along z direction.
515P) Calculate (r is the usual position vector: (coser), (ri), 7 x(x B) where B is constant vector along z direction.
(i) Consider the wave Ē(7,t) = Ło cos(wt – k ), where Ē, is a fixed vector. Determine the relation between w and k = \KI SO that Ē(7,t) is a solution of the wave equation -27 182 VPE = 2 ət? - What is the direction of propagation of the wave? ii) Show, by substitution of Ē(7,t) in the appropriate Maxwell's equation, that K· Ē= 0. iii) Assuming that the magnetic field B(7, t) = B, cos(wt – K:1),...
Find the curl of the vector.
Find the curl of the following vector field: t-y where b is a constant and r = x-+y +z
general relativity question.
Instructions The first problem is just a test of how well one knows the methods of averaging over directions. This is a standard tool which is used in many areas of classical electrodynamics and general relativity. e.g, in the context of the radiation problem and in the context of particle motion in inhomogeneous electromagnetic fields. The second problem is just a test of how well one understood the content of the present lecture. Solve the problems and...
A strong light bulb radiates light in all directions. The average power of the EM waves by this bulb is 1910.0 W. At a distance r = 0.6 m from the bulb, the EM waves spread over a surface area of 4πr2 (a) Calculate the Average Intensity. Keep 1 decimal place. (b) Calculate the Average Energy Density (including both the electric field and the magnetic field). Write the result in terms of 10-5J/m3. Keep 4 decimal places.(c) Calculate the Average (rms) Electric...
all of the questions
Quis 7 Naine Directions: Write out your legible wwers in t It a partiele is oving I is its pericd 2. I the total acceleration of an object is 60 m/s2 and its rudial neceleration is 30 m/s due sousth what is tarigential acceleration of the object and the direction of the object? A car moving with a constant acceleration that started from rest goes over a bump, which has a magnitude of the total acceleration...
Let V be the vector space of all sequences over R. Given (a1, a2, T,U V V by ) e V, define : ) ...) = (0, a1, 0, a2, 0, a3, . . . ) Тај, а2, аз, ад, 0, аз, (a1, a3, a5,.) and U(a1, a2, a3, a4, (a) Find N(T) and N(U) (b) Explain why T is onto, but not 1-1 (c) Explain why U is 1-1, but not onto.