A sensor apparatus comprises an electrically conductive chip carrier comprising a busbar, a first connection and a second connection, and a differential magnetic field sensor chip which is arranged on the chip carrier and has two sensor elements. The form of the busbar is such that a measurement current path running from the first connection to the second connection through the busbar comprises a main current path and a bypass current path, wherein the main current path and the bypass current path run parallel to one another, and a bypass current flowing through the bypass current path is less than a main current flowing through the main current path. The magnetic field sensor chip is configured to capture a magnetic field induced by the bypass current.