Electromagnetism

F = qv x B

When to use:

• Moving charged particle in magnetic field

• Keywords:

  • “electron/proton moving…”

  • “enters magnetic field”

  • “force on charge”

Triggers:

• Velocity given → use cross product

• Angle given → use:

  • F = qvBsinθ

F = IL x B

When:

• Current-carrying wire in B-field

Triggers:

• “segment of wire”

• “current = … A”

• “force on wire”

Fb = Fc

• Radius:

r=mvqBr

• Frequency:

f=qB/2πm

Triggers:

• “circular path”

• “bubble chamber”

• “radius of orbit”

v = E/B

Triggers:

• “undeflected particle”

• BOTH electric and magnetic field

τ=NIABsinθ

Triggers:

• “loop rotating”

• “torque”

• “axis”

dB=μ0​​Idlsinθ/4pir²​

When:

• Weird shapes (arcs, triangles, partial loops)

Triggers:

• “arc”

• “finite wire”

• “triangle loop”

B = u0I/2R

Triggers:

• “circular loop”

• “center of loop”

B = u0Itheta/4piR

Triggers:

• “arc with angle θ”

• not full circle

B = u0I/2pir

Triggers:

• “long wire”

• “infinite wire”

Integral Bdl = u0Ienc

When:

ONLY if symmetry:

• infinite wire

• solenoid

• toroid

• cylinder

Triggers:

• “uniform distribution”

• “inside wire”

• “toroid”

• “solenoid”