If an electron is in a region with an electric potential of +8 V, can its future motion be predicted from this information alone?

If an electron is in a region with an electric potential of +8 V, can its future motion be predicted from this information alone?

• A. Yes, it will accelerate toward lower potential
• B. Yes, it will accelerate toward higher potential
• C. There is not enough information to predict its motion
• D. It will come to rest

Answer: (C)

The ability to predict motion comes from the electric field, not just the value of the potential at a point. The electric field is E = -∇V, the spatial rate of change of the potential. Knowing that the electron sits in a region with V = +8 V tells you its potential energy is U = qV = -e × 8 V, but it provides no information about how V changes in space around it. Without the gradient of V, you don’t know the force acting on the electron (F = qE) or how the velocity will change. The initial velocity and any other forces also matter. If the potential were uniform in that region (no gradient), there would be no force and the motion would simply continue as it is. Since you only know a single potential value, there isn’t enough information to predict the future motion.

The ability to predict motion comes from the electric field, not just the value of the potential at a point. The electric field is E = -∇V, the spatial rate of change of the potential. Knowing that the electron sits in a region with V = +8 V tells you its potential energy is U = qV = -e × 8 V, but it provides no information about how V changes in space around it. Without the gradient of V, you don’t know the force acting on the electron (F = qE) or how the velocity will change. The initial velocity and any other forces also matter. If the potential were uniform in that region (no gradient), there would be no force and the motion would simply continue as it is. Since you only know a single potential value, there isn’t enough information to predict the future motion.