Problem 4E

Use mathematical induction to show that if is an eigenvalue of Am, with x a corresponding eigenvector.

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