The watt balance is operated in two asynchronous measurement modes to obtain the voltage–velocity ratio U/v and the force–current ratio mg/I, respectively. The magnetic flux density will change between the two modes when the effect due to the coil current is taken into account, particularly for watt balances using a soft magnetic material in the magnetic circuit. Normally, the linear component of the magnetic flux density change can be easily eliminated by reversing the coil current; however, the quadratic component remains as a systematic error, ie a non-linear error. In this paper, we use a theoretical analysis and a differential finite element method to investigate the behaviour of the quadratic dependence in a typical magnetic circuit. Several strategies are discussed to minimize this error in the magnetic system design for the watt balance.