(a) Write an expression for the force acting on a charge q moving with velocity v in an electric field E and magnetic field B. (b) A charged particle of mass m and charge q is accelerated through a potential difference of V and then injected into a region with a magnetic field B perpendicular to the plane in which the charge moves. Derive an expression for the radius of curvature, r , of the path of the particle when in the magnetic field. 13.15 In a certain mass spectrometer the magnetic field has a magnitude of 0.2 T. It is intended that this spectrometer be used to separate two isotopes of uranium, 235U92(mass 3.90x10^(-25) kg) and 238U92(mass 3.95x10^(-25) kg). In order to be separated the radii of curvature described by singly charged (charge +e) ions must differ by 2 mm. Calculate the electric potential through which the ions must be accelerated in order to achieve this.