the Lorentz force is the same as for an electric field, the carrier velocity v is given by: where μ is the carrier mobility. Solving for the velocity, we find: where the effective reduction in mobility due to the B-field (for motion perpendicular to this field) is apparent. Electric current (proportional to the radial component of velocity) will decrease with increasing magnetic field and hence the resistance of the device will increase. Critically, this magnetoresistive scenario depends sensitively on the device geometry and current lines and it does not rely on magnetic materials. In a semiconductor with a single carrier type, the magnetoresistance is proportional to (1 + (μB)2), where μ is the semiconductor mobility (units m2·V−1·s−1 or T −1) and B is the magnetic field (units teslas). Indium antimonide, an example of a high mobility semiconductor, could have an electron mobility above 4 m2·V−1·s−1 at 300 K. So in a 0.25 T field, for example the magnetoresistance increase would be 100%. Anisotropic magnetoresistance (AMR) Thomson's experiments are an example of AMR, a property of a material in which a dependence of electrical resistance on the angle between the direction of electric current and direction of magnetization is observed. The effect arises from the simultaneous action of magnetization and spin-orbit interaction and its detailed mechanism depends on the material. It can be for example due to a larger probability of s-d scattering of electrons in the direction of magnetization (which is controlled by the applied magnetic field). The net effect (in most materials) is that the electrical resistance has maximum value when the direction of current is parallel to the applied magnetic field. AMR of new materials is being investigated and magnitudes up to 50% have been observed in some ferromagnetic uranium compounds. In polycrystalline ferromagnetic materials, the AMR can only depend on the angle between the magnetization and current direction and (as long as the resistivity of the material can be described by a rank-two tensor), it must follow where is the (longitudinal) resistivity of the film and are the resistivities for and , respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed (somewhat confusingly[1]) the planar Hall effect. In monocrystals, resistivity depends also on individually. To compensate for the non-linear characteristics and inability to detect the polarity of a magnetic field, the following structure is used for sensors. It consists of stripes of aluminum or gold