Malamala
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Hello! I have a parallel plate capacitor (we can assume that the plates are circular) and I apply a time varying voltage to it, such that the electric field inside is ##E_0\sin \omega t##. If I use the Maxwell equations, I get for the magnetic field
$$B(t) = \frac{\omega E_0}{2c^2}r\hat{r}$$
so the magnetic field increases with the radius, and it is in the radial direction. However, I am not sure I understand how to define ##r=0##. Naturally, I could take that at the center of the plates, such that the magnetic field at the center is zero. But I am not sure why I need to do that. If I take a small (imaginary) circular loop and apply Maxwell's equations to that, I would still get ##B(t) = \frac{\omega E_0}{2c^2}r\hat{r}##, regardless of where I place that loop. Thus it seems (ignoring edge effects, which should be ok if I assume that I look at small enough loops and the plates are large) that the magnetic field is zero everywhere inside the capacitor, as I can take the center of this loop at any point inside. What am I missing? Why can't I apply this formalism to any loop in between the 2 plates?
$$B(t) = \frac{\omega E_0}{2c^2}r\hat{r}$$
so the magnetic field increases with the radius, and it is in the radial direction. However, I am not sure I understand how to define ##r=0##. Naturally, I could take that at the center of the plates, such that the magnetic field at the center is zero. But I am not sure why I need to do that. If I take a small (imaginary) circular loop and apply Maxwell's equations to that, I would still get ##B(t) = \frac{\omega E_0}{2c^2}r\hat{r}##, regardless of where I place that loop. Thus it seems (ignoring edge effects, which should be ok if I assume that I look at small enough loops and the plates are large) that the magnetic field is zero everywhere inside the capacitor, as I can take the center of this loop at any point inside. What am I missing? Why can't I apply this formalism to any loop in between the 2 plates?