Ørsted's law only holds for steady currents, which don't change with time. Therefore, it only holds for DC electric circuits, with no capacitors or inductors. It can be seen that it fails for time varying currents by considering the case of a circuit consisting of a battery charging a capacitor through a resistor. It can be verified experimentally that the current in this circuit creates a magnetic field, yet any closed curve encircling the conductor can be spanned by a surface passing between the capacitor plates, through which no current passes, from which the equation would give zero magnetic field. Ørsted's law was modified by Maxwell to cover the case of time-varying currents by adding a new source term called displacement current, giving the Ampere–Maxwell equation.