Physics
Physics
Problem
A positive test charge moves along the x-axis through a region where the electric potential decreases uniformly from 6.0 V at x = 0 cm to 2.0 V at x = 4.0 cm, then increases uniformly to 7.0 V at x = 8.0 cm. Identify the interval(s) during which the charge’s speed is increasing.Intuitive explanation
The key is recognizing that a positive charge accelerates when the electric field points in the direction of motion—that is, when the charge moves toward lower potential. Break the path into two segments and find the potential gradient (field direction) in each: from 0–4 cm the potential decreases, so the field points in the +x direction and does positive work on a positive charge moving rightward; from 4–8 cm the potential increases, so the field points in the −x direction and opposes rightward motion. The charge speeds up only where the field aids its motion.
Intuitive explanation
The key is recognizing that a positive charge accelerates when the electric field points in the direction of motion—that is, when the charge moves toward lower potential. Break the path into two segments and find the potential gradient (field direction) in each: from 0–4 cm the potential decreases, so the field points in the +x direction and does positive work on a positive charge moving rightward; from 4–8 cm the potential increases, so the field points in the −x direction and opposes rightward motion. The charge speeds up only where the field aids its motion.