Question

In: Physics

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

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

Solutions

Expert Solution


Related Solutions

Consider the retarded scalar and vector potentials. Show that they satisfy the Lorentz gauge.
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
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...
2) Consider the Lorentz transformation that maps (x,t) into (x',t'), where t and x are both in time units (so x is really x/c) and all speeds are in c units also. a) Show that the inverse of the Lorentz transformation at v is the same as the Lorentz transformation at -v. Why is that required? b) Show that x^2 - t^2 = x'^2 - t'^2, i.e., that x^2 - t^2 is invariant under Lorentz transformation
derive the classical wave equation. Show the relationship between this equation and the electromagnetic wave equation.
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
Consider the following wave equation for u(t, x) with boundary and initial conditions defined for 0...
Consider the following wave equation for u(t, x) with boundary and initial conditions defined for 0 ≤ x ≤ 2 and t ≥ 0. ∂ 2u ∂t2 = 0.01 ∂ 2u ∂x2 (0 ≤ x ≤ 2, t ≥ 0) (1) ∂u ∂x(t, 0) = 0 and ∂u ∂x(t, 2) = 0 (2) u(0, x) = f(x) = x if 0 ≤ x ≤ 1 1 if 1 ≤ x ≤ 2. (a) Compute the coefficients a0, a1, a2, ....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT