**Conservative Forces and Work Done over a Closed Loop**

In physics, a conservative force is a type of force that depends only on the initial and final positions of an object, and not on the path taken by the object. This means that the work done by a conservative force over any closed loop is zero.

**Explanation:**

To understand why the work done over a closed loop by a conservative force is zero, let's consider the definition of work done. Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force.

If a force is conservative, it can be expressed as the negative gradient of a scalar potential function. This means that the force can be written as the negative derivative of a potential energy function with respect to position.

Now, let's consider a closed loop. Since the starting and ending positions are the same, the change in potential energy over the loop is zero, as the potential energy depends only on the position. This implies that the change in potential energy is equal to the negative of the work done by the conservative force over the loop.

Since the change in potential energy is zero, the work done by the conservative force over the closed loop must also be zero. This means that the net work done by the conservative force in completing a closed loop is zero, regardless of the path taken.

**Example:**

For example, consider a ball moving in a gravitational field. The gravitational force is conservative, as it depends only on the position of the ball. If the ball is lifted to a certain height and then allowed to fall back to the starting position, the work done by the gravitational force over the closed loop is zero. This is because the potential energy at the starting and ending positions is the same, regardless of the path taken by the ball.

**Conclusion:**

In conclusion, for conservative forces, the work done over a closed loop is zero. This is because conservative forces can be expressed as the negative gradient of a potential energy function, and the potential energy depends only on the position of the object. Therefore, the change in potential energy over a closed loop is zero, resulting in zero work done by the conservative force.

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