Arc voltage is a crucial parameter that characterizes the breaking performance and electrical lifespan of DC circuit breakers. For effective arc voltage observation in operational breakers, non-contact and non-intrusive methods are essential. This paper investigates the relationship between arc voltage and the near-field magnetic flux around the arc. Through experimental analysis, the characteristics of the arc during the arc initiation, arcing, and arc quenching stages are examined. A clear relationship between arc voltage, current, and near-field magnetic flux is established. The following conclusions are drawn: under repeated breaking tests, the relationship between arc voltage and current exhibits a one-to-many pattern due to variations in the cutoff value and the presence of both linear and nonlinear regions. Additionally, in the low-frequency range, the normalized near-field magnetic flux shows an approximately linear relationship with arc voltage, which can be expressed using a piecewise function. This prospectively enables the estimation of arc voltage variations in the low-frequency range.