Show that in Lorentz gauge the electric potential ?(x, t) satisfies the wave equation.

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genius_generous answered 3 years ago

Starting with Maxwell's equations show that the magnetic field satisfies the same wave equation as the...

Starting with Maxwell's equations show that the magnetic field satisfies the same wave equation as the electric field. in particular, that is, too, propagates with the same speed.

Consider the retarded scalar and vector potentials. Show that they satisfy the Lorentz gauge.

show the velocity and direction while proving that s(x,t) = Aexp[-(4x+6t)^2] is a wave equation

2) Consider the Lorentz transformation that maps (x,t) into (x',t'), where t and x are both...

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derive the classical wave equation. Show the relationship between this equation and the electromagnetic wave equation.

A mechanical wave is given by the equation: y(x,t) = 0.5 cos (62.8x – 15.7t) ,...

A mechanical wave is given by the equation: y(x,t) = 0.5 cos (62.8x – 15.7t) , Find: (1) Amplitude, frequency, wavelength? (2) The velocity of the wave? (3) The maximum velocity of the vibrations? (4) Write down the equation in the opposite direction?

Consider the following one-dimensional partial differentiation wave equation. Produce the solution u(x, t) of this equation....

Consider the following one-dimensional partial differentiation wave equation. Produce the solution u(x, t) of this equation. 4Uxx = Utt 0 < x 0 Boundary Conditions: u (0, t) = u (2π, t) = 0, Initial Conditions a shown below: consider g(x)= 0 in both cases. (a) u (x, 0) = f(x) = 3sin 2x +3 sin7x , 0 < x <2π (b) u (x, 0) = x +2, 0 < x <2π

1. What is the highest value of x that satisfies this equation x(x+4) = -3

1. What is the highest value of x that satisfies this equation x(x+4) = -3 A. -1 B. 0 C. 1 D. -3 2. If x2 - 9x = -18, what are the possible values of x? A. -3 and -6 B. -3 and 6 C. 3 and -6 D. 3 and 6 3. What polynomial can be added to 2x2 - 2x+6 so that the sum is 3x2+ 7x? A. 5x2+ 5x+ 6 B. 4x2+ 5x+ 6 C....

Solve the wave equation, a2 ∂2u ∂x2 = ∂2u ∂t2 0 < x < L, t...

Solve the wave equation, a2 ∂2u ∂x2 = ∂2u ∂t2 0 < x < L, t > 0 (see (1) in Section 12.4) subject to the given conditions. u(0, t) = 0, u(π, t) = 0, t > 0 u(x, 0) = 0.01 sin(9πx), ∂u ∂t t = 0 = 0, 0 < x < π u(x, t) = + ∞ n = 1

Solve the wave equation ∂2u/∂t2 = 4 ∂2u/∂x2 , 0 < x < 2, t >...

Solve the wave equation ∂2u/∂t2 = 4 ∂2u/∂x2 , 0 < x < 2, t > 0 subject to the following boundary and initial conditions. u(0, t) = 0, u(2, t) = 0, u(x, 0) = { x, 0 < x ≤ 1 2 − x, 1 < x < 2 , ut(x, 0) = 0

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