The equilibrium position of objects in any field corresponds to situation of

1. Analyze the question The question asks which energy condition corresponds to the equilibrium position of an object in a field (gravitational, electric, etc.).

2. Explain the concept In a force field, the force on an object is related to the potential energy by:

F = −dU/dx

At equilibrium, the net force is zero, so dU/dx = 0. This means the potential energy is at a stationary point (either a minimum or a maximum). There are three types of equilibrium:

• Stable equilibrium: U is at a minimum. If the object is displaced slightly, a restoring force pushes it back (e.g., a ball at the bottom of a bowl).
• Unstable equilibrium: U is at a maximum. A small displacement makes it move further away (e.g., a ball balanced on top of an upturned bowl).
• Neutral equilibrium: U is constant (e.g., a ball on a flat table).

3. Solve by checking the options

• A. Equipotential energy: this describes neutral equilibrium only, not the general case.
• B. Maximum potential energy: this describes unstable equilibrium only. The object will not stay there if disturbed.
• C. Minimum potential energy: this describes stable equilibrium, which is the standard position an object settles into in a field. Systems naturally move toward the lowest potential energy and stay there.
• D. Minimum kinetic energy: kinetic energy relates to motion, not position in the field, so it does not define equilibrium.

4. Answer The equilibrium position an object settles into in a field corresponds to minimum potential energy, which is option C.

5. Exam tip Think of a ball rolling into a valley: it comes to rest at the lowest point, where potential energy is smallest. "Stable = Smallest PE." Be careful, though: if a question specifically says "unstable equilibrium," the answer is maximum PE.