B

Step 1: Understand Thomson's method in determining e/m of electrons, where e is the charge and m is the mass of the electron.
Step 2: In this method, an electron beam is subjected to both electric and magnetic fields.
Step 3: For the forces to correctly influence the motion of the electrons and allow for a precise determination of the charge-to-mass ratio, the electric field (E) and the magnetic field (B) must be arranged such that they are perpendicular to each other and also perpendicular to the direction of the electron beam.
Step 4: This perpendicular configuration allows the use of the Lorentz force law, where the net force on the electrons is the vector sum of the electric force and the magnetic force, facilitating the calculation of e/m.
Therefore, the correct answer is B.