A steady current requires a non-zero current density everywhere in a closed loop, yet electrostatic fields satisfy the conservative condition $\oint \mathbf{E}\cdot d\mathbf{l} = 0$. What physical consequence follows for sustained circulation?

A. A non-electrostatic field must perform net work along the loop

Electrostatic fields cannot sustain circulation because their closed line integral vanishes, meaning charges gain no net energy over a complete circuit without a non-conservative source. Confusing steady currents with zero resistance or zero internal field ignores how Ohm's law and dissipation operate.