Final answer:
The speed of an ion in perpendicular electric and magnetic fields with zero acceleration is found by equating the electric force to the magnetic force and solving for the velocity. Upon substituting the given values for the fields into the equation v = E/B, the velocity is calculated to be 6.25×10´ m/s, which does not match any of the provided options.
Step-by-step explanation:
The student's question pertains to the motion of an ion in the presence of perpendicular electric and magnetic fields with the condition that the ion's acceleration is zero. To find the speed of the ion at which its acceleration is zero, we can apply the principle that the electric force must be balanced by the magnetic force, since only under that condition will the net force and hence the acceleration be zero. The electric force (Fe) is given by Fe = qE, and the magnetic force (Fm) is given by Fm = qvB, where q is the charge of the ion, E is the electric field strength, v is the velocity of the ion, and B is the magnetic field strength. Setting Fe equal to Fm and solving for v, we get v = E/B.
Substituting the given values, E = 5×104 V/m and B = 0.8 T, the speed v = (5×104) / (0.8) = 6.25×104 m/s. This result does not match any of the options provided in the question. Therefore, it seems there may be a mistake in the given options or the interpretation of the question. However, the principle demonstrated here is crucial in physics, especially in the context of the motion of charged particles in electric and magnetic fields.