# Does a Static $E$-field Increase the Gauge Invariant Vector Potential Without Bound?

Indicates that the transverse electric field is the time derivative of the transverse vector potential.

This gauge invariant vector potential increases without bound as long as there exists a static electric field. Indeed, even when the electric field is removed, there appears to be no mechanism by which the gauge invariant vector potential disappears.

In what way am I misinterpreting (7.13)?

• A transverse electric field requires a changing current, so I think we need not worry about unbounded growth in the vector potential, because that requires an unbounded increase in current density. – user27118 Mar 23 '15 at 19:58