a) Determine which amounts of postage can be formed using just 3-cent and 10-cent stamps.

b) Prove your answer to (a) using the principle of mathematical induction. Be sure to state explicitly your inductive hypothesis in the inductive step.

c) Prove your answer to (a) using strong induction. How does the inductive hypothesis in this proof differ from that in the inductive hypothesis for a proof using mathematical induction?

PHY 184 Week 9 Notes-Magnetic Fields & Electromagnetic Induction 10/24-10/27 Moving charges produce a magnetic field o The Biot-Savart Law establishes this relation Wires produce a magnetic field o Can be seen by a compass near the wires μ d B= 0 ids×^ ⏞= ⃗ o 4π r2 ; r μ0 is the magnetic permeability of free space 4π 10 -7 To calculate B at P just integrate along the path Solving for B using symmetry gives B= μ0i o 2πd 2 Parallel Wires Consider a wire with current i a d1stance d away, with another wire nearby with current i .2 o They will attract Magnetic Force is given by F=i2L B1si