Equation E17.7 $\frac{1}{\mu_{0} \varepsilon_{0}} \frac{\partial^{2} B_{y}}{\partial x^{2}}-\frac{\partial^{2} B_{y}}{\partial t^{2}}=0 \quad$ is also solved by a function $f(s)$, where $s=t+x / c$.

Question

Quizplus · Accepted Answer

The given equation resembles the wave equation for electromagnetic waves in vacuum, where $\mu_0$ is the permeability of free space, $\varepsilon_0$ is the permittivity of free space, and $c = 1/\sqrt{\mu_0 \varepsilon_0}$ is the speed of light in vacuum. A function $f(s)$, where $s = t + x/c$, represents a wave moving in the +x direction and satisfies the wave equation, indicating that the equation can indeed be solved by such a function. This is because the derivatives with respect to $x$ and $t$ will transform into derivatives with respect to $s$, maintaining the form of the wave equation.

Equation E17 1μ0ε0∂2By∂x2−∂2By∂t2=0\frac{1}{\mu_{0} \varepsilon_{0}} \frac{\partial^{2} B_{y}}{\partial x^{2}}-\frac{\partial^{2} B_{y}}{\partial t^{2}}=0 \quadμ0​ε0​1​∂x2∂2By​​−∂t2∂2By​​=0 Is Also Solved by a Function

Equation E17 $\frac{1}{\mu_{0} \varepsilon_{0}} \frac{\partial^{2} B_{y}}{\partial x^{2}}-\frac{\partial^{2} B_{y}}{\partial t^{2}}=0 \quad$ Is Also Solved by a Function