# Is there a magnetic field between capacitor plates while the capacitor is charging?

(Edit, Question was previously: "Can a changing electric field produce a magnetic field?")

I've just began studying Maxwell's equations today and what really had my attention is Ampere's law, the second term in particular. $$\int\vec B \cdot d\vec l=μ_0I_{encl}+μ_0ε_0\frac{dΦ_E}{dt}$$ Does this mean that a changing electric field can cause a magnetic field? For example, during the charging of a capacitor, between the plates where the electric field is changing.

I saw an exercise example where we changed the voltage across a capacitor and thus created a magnetic field.But some websites state that as long as there is no current - charge movement , there is no magnetic field being created. I read the same about the capacitor in particular. Could the example be wrong or is there a difference ?

## 2 Answers

But some websites state that as long as there is no current - charge movement , there is no magnetic field being created.

This is incorrect. Light propagation happens because a changing electric field can produce a magnetic field just like a changing magnetic field produces an electric field. Your initial conclusion is correct: a changing electric field is as much a source of magnetic field as current is.

So yes, there is a magnetic field in a capacitor while it is being charged. Once the charging is complete and the electric field becomes constant, it vanishes.

• Light propagation?Where can I learn about this? Thanks by the way. – John Katsantas Jan 27 '17 at 8:37
• Read any book about electrodynamics (or an optics book where the fields related to light are discussed). Perhaps try Griffiths. – Raziman T V Jan 27 '17 at 8:41

I will try to put this very simply. As we know, a straight current carrying wire produces a magnetic field encircling the conducting wire. Also, as theoreticaly suggested, a displacement current is set up between the plates of the capacitor when there is a change in electric field (generally due to change in charge that appears on the plate). So, similarly, we can consider a magnetic field associated with the displacement current too.