We propose a new formulation for the forward problem in magnetic induction tomography (MIT). We formulate the problem in terms of interior and exterior boundary integral equations (BIEs), subject to appropriate boundary conditions. We then transform a standard exterior BIE involving the magnetic vector potential to a BIE involving the electric fields. This transformation eliminates two boundary conditions involving the magnetic vector potential and its normal derivative. This greatly reduces the computational complexity of the model. Here, we compare numerical solutions of the model to analytical solutions.