Phys 226 Magnetic Fields

F_B=|q|vBsinθ

use when charge moves through a magnetic field

F_B=|q|vB

charge moving through magnetic field and velocity is perpendicular

steps to find magnetic force on a moving charge + what is the R hand rule

1. find q (charge, Coulombs), v, B (Mag field, Tesla) and angle

2. calculate magnitude F_B=|q|vBsinθ

3. use R hand rule for direction (for positive charge: fingers=velocity, curl=mag field, thumb=force — neg charge is the opposite direction of this)

F_B=ILBSinθ

Magnetic force non a current-carrying wire Mag Force (Newtons)=Current (Amperes) x Length of wire (meters) x Mag Field (Tesla) x sin(angle btw wire direction and B field)

B=µ₀I/2πr

Magnetic field from a straight wire, Mag Field (Tesla) = constant x Current (Amperes) / 2π x distance from wire (meters)

B=µ₀nI

Magnetic Field inside solenoid/coil Mag field (Tesla) = constant x # of turns x Current (Ampere)

B=µ₀I_enclosed/2πr

Amperes Law

Steps for Amperes Law + R Hand rule

1. draw and amperian loop, circle around the current

2. determine enclosed Current (outside wire → I_enc=I) (inside wire/cylinder → I_enc=E r²/R²)

3. use B=µ₀I_enclosed/2πr and solve for B

4. direction with R hand rule (thumb=current, fingers=mag field direction)