here since it is question of advance physics so please lool at the standard solution to solve such differential equation, that will give the electric field.
Given the following: B vector = B_0 alpha [(yzt omega)i^hat (xz omega t) j^hat + (y^2...
H08.2 (2 points) Given the vector velocity field V(x, y, z, t) = 4t i + xz j + 2ty3 k a) Is this a valid incompressible flow field? b) Is this flow field irrotational?
A displacement vector is given: r=(2.3m) i hat +(5.4m/s^2) t^2 j hat- (3.0m/s^3) t^3 z hat a. Find the displacement from t=0 s to t=3.0 s. b. Find the velocity vector. c. Find the average velocity from t = 0 s to t = 3.0 s. d. Find the acceleration vector.
Given the following: B bar = (0.5 x^2 yt^2 T)j^- (1.2x y^2 t T)k^, a) Determine the curl of the magnetic field. b) Determine the electric field.
Question 2: For an electromagnetic plane wave, the electric field is given by:$$ \vec{E}=E_{0} \cos (k z+\omega t) \hat{x}+0 \hat{y}+0 \hat{z} $$a) Determine the direction of propagation of the electromagnetic wave.b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave \(\vec{B}\).c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense?d) If the amplitude of the magnetic field was measured to be \(2.5 * 10^{-7} \mathrm{~T}\),...
Algebraically sum the two electric field waves E1=E01cos([omega]t + [alpha]1) and E2=E02([omega]t +[alpha]2) under the condtions E02=E01 and aplha1=0. Your result should be a single harmonic (sine or cosine) function with appropriate amplitude and phase. Express the amplitude and phase in terms of parameters of the two combined waves.
3) Given vector field F(x,y,z)=<y, xz,x? >. Find N dr where T is the path around the triangle with vertices (1,0,0),(0,1,0) and (0,0,1) traced counterclockwise (when viewed from above.)
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
Evaluate the line integral ∫ F *dr where C is given by the vector function r(t). F(x, y, z) = (x + y2) i + xz j + (y + z) k, r(t) = t2i + t3j − 2t k, 0 ≤ t ≤ 2
Evaluate the line integral ∫C.F·dr, where C is given by the vector function r(t).F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t3 i- t3j + tk, 0 ≤ t ≤ 1 .
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...