A new method for reconstructing electrical properties from $$$B_1^+$$$ data based on Maxwell's equations in an E polarized field (found in the midplane of a birdcage coil) is presented. This first-order EPT (foEPT) method uses first order spatial derivatives as opposed to the second order Helmholtz based MR-EPT methods and is thus less susceptible to noise. Furthermore, the method does not rely on any homogeneity assumptions. The method is validated using an in-vivo phantom measurement and compared to an MR-EPT reconstruction. FoEPT conductivity reconstructions show less noise-amplification and less boundary artefacts compared to Helmholtz-based MR-EPT reconstructions.