Maxwell’s equations relating the electric field E and magnetic field H as they vary with time in a region containing no charge and no current can be stated as follows:
where c is the speed of light. Use these equations to prove the following:
(a)
(b)
(c)
(d)
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Chapter 16 Solutions
Multivariable Calculus
- Using the Bode plot shown below, estimate the frequency response to the following inputs: a) u(t)= 3 cos 4t b) u(t) 0.5 sin 40t c) u(t)= 10 cos 400t After doing the above, derive the transfer function for the system that has this Bode plot. Magnitude (dB) Phase (degrees) -20 -30 -40 -50 10⁰ 0 -15 -30 -45 -60 -75 -90 100 10¹ 101 Frequency 10² 10² 103 103arrow_forwardAb. 56 Advanced matharrow_forward(b) In the same figure, find the electric flux through the plane surface if 0 = 60°, E = 350 N/C, and d = 5 cm. The electric field is uniform over the entire area of the surface. E darrow_forward
- Determine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point Oarrow_forwardShow if the function is a wave function or not.arrow_forwardCorsider the dtere ntial equetions 2. a) Show that x° and Ygu are linearly Independent Salutions Of this equation On the Interual OLXL b) Write damn the general solution of the given equation (le) tind the Solution that Satiesties the condition y(2)= 3 ard y'(2) = -1arrow_forward
- Base on the graph, make a conjecture about whether the circulation and flux of F = ( − x, − y) on C:F(t) = (4 cos(t), 4 sin(t)) for 0 ≤ t ≤is positive, negative, or zero. Then a. Compute the circulation and interpret the result. Circulation = Preview b. Compute the flux and interpret the result. Flux = Preview Get help:arrow_forwardThe behaviour of a swinging door can be modelled by the second order, constant coefficient ODE d²0 b de k + I dt I dt² (1) where (t) gives the angular position of the door, and I, b, k are positive mechanical parameters that affect the motion of the door. wall door (i) (a) Substitute ( Ө + = 0 wall e(t) = = et into equation (1) to find the characteristic equation. (b) Determine the relationship between I, b, and k that will ensure the roots of the characteristic equation are not complex. That is, we seek solutions that have no oscillatory behaviour. (c) State the general solution corresponding to the case of repeated real roots in (b). (ii) (a) Letting y₁(t) = : 0(t) and y₂(t) = 0'(t) = y₁ (t), show that equation (1) can be written as a system of first order ODEs involving y₁ and Y2. Summarise the system in the matrix equation y' = M y. (b) Show that the eigenvalues of M are identical to the roots computed in (i)(b). (c) Find the eigenvector for the case of repeated eigenvalues. For…arrow_forwardHandwritten onlyarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage