Savchenko Problem 9.2.15
Physics
Problem
a. The metal ring broke when the current in the ring was I . They made 0 exactly the same ring, but from a material whose ultimate strength is ten times greater. What current will break the new ring? b. What current will break a new ring made of this stronger material, if all the dimensions of the new ring are twice the size of the old one?Intuitive explanation
The breaking current depends on how magnetic force scales with the ring's physical properties. The magnetic force on a current-carrying loop is proportional to and the ring's cross-sectional area, while the material's ability to withstand stress depends on its ultimate strength and cross-sectional area. By balancing these, you can find how the breaking current changes when strength or size changes.
Intuitive explanation
The breaking current depends on how magnetic force scales with the ring's physical properties. The magnetic force on a current-carrying loop is proportional to and the ring's cross-sectional area, while the material's ability to withstand stress depends on its ultimate strength and cross-sectional area. By balancing these, you can find how the breaking current changes when strength or size changes.