A proton is placed midway between points A and B. The...

A proton is placed midway between points $A$ and $B$. The potential at point $A$ is $-20 \mathrm{~V}$, and the potential at point $B$ $+20 \mathrm{~V}$. The potential at the midpoint is $0 \mathrm{~V}$. The proton will a) remain at rest. b) move toward point $B$ with constant velocity. c) accelerate toward point $A$. d) accelerate toward point $B$. e) move toward point $A$ with constant velocity.

A proton is placed midway between points $A$ and $B$. The potential at point $A$ is $-20 \mathrm{~V}$, and the potential at point $B$ $+20 \mathrm{~V}$. The potential at the midpoint is $0 \mathrm{~V}$. The proton will
a) remain at rest.
b) move toward point $B$ with constant velocity.
c) accelerate toward point $A$.
d) accelerate toward point $B$.
e) move toward point $A$ with constant velocity.

Key Concepts

Electric Potential

Electric potential is a scalar quantity that represents the potential energy per unit charge at a point in an electric field. It tells us how much work is needed to bring a unit charge from a reference point (typically infinity) to that point. Although a point may have zero potential, this does not imply the absence of an electric field or force acting on a charge at that location.

Electric Field

The electric field is a vector quantity defined as the negative gradient of the electric potential. It determines the force experienced by a charge placed in the field. A non-zero gradient in the potential means that there will be a corresponding electric field, and thus a charged particle placed at a point—regardless of the potential value—can experience a force if the gradient is non-zero.

Force on a Charged Particle

For a particle with charge q, the force experienced in an electric field is given by F = qE. The direction of force on a positive charge is the same as the direction of the electric field. This means that even if the electric potential at a point is zero, a positive charge will be accelerated in the direction where the potential decreases (lower potential energy region) due to the influence of the electric field.

Potential Energy

Potential energy in an electric context is calculated by multiplying the charge by the electric potential at a given point (U = qV). A charged particle will naturally move towards regions of lower potential energy. For a positive charge, this means moving towards regions of lower electric potential, as the system tends to minimize its energy.

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