When you bring a positive test charge near a negatively charged ball, an attractive electrostatic force acts between them due to their opposite charges. As you move the test charge closer to the negatively charged ball, several concepts related to electric fields and potential energy come into play.
-
Electric Field: The negatively charged ball creates an electric field in the space surrounding it. The direction of this electric field is towards the ball, indicating that a positive test charge would experience a force directed towards the ball.
-
Force: As you move the positive test charge closer to the ball, the attractive electrostatic force acting on the test charge increases. The strength of the force is inversely proportional to the square of the distance between the charges (according to Coulomb's Law). Hence, as the test charge approaches the negatively charged ball, the force pulling it closer becomes stronger.
-
Potential Energy: The potential energy \( U \) associated with the system of the positive test charge and the negatively charged ball decreases as you bring the test charge closer. This is because potential energy is defined as the work done against the electric force to separate the charges. As the test charge gets closer, the system becomes more stable, resulting in a decrease in potential energy.
-
Potential Difference: The potential difference \( V \) in an electric field is related to the position of the charge within that field. As the test charge moves from a position farther from the negatively charged ball to a position closer to it, it moves through a region of varying electric potential. The region nearer to the negatively charged ball has a lower electric potential compared to regions farther away.
-
Work: The work \( W \) done on the test charge as it moves closer to the ball is negative when considering the work done by the electric field. When the test charge moves in the direction of the electric field (towards the negatively charged ball), the electric field does positive work on the test charge, causing the test charge to gain kinetic energy as it accelerates towards the ball.
In summary, as you move a positive test charge closer to a negatively charged ball, the force acting on it increases, the potential energy of the system decreases, the electric potential becomes lower, and work is done by the electric field on the test charge, increasing its kinetic energy. The overall interaction illustrates the principles of electrostatics inherent in electric forces and fields.