Magnetism

Magnetic Force of a Charged Particle

F_mag = |q|vBsin(θ)

Right hand rule for F_mag, v, B

Charged particle in magnetic field (B)

• Charge spins in circles

• Opposite charge would make F_mag in opposite direction

Can a magnetic field (B) do work on a particle?

Radius of particle path

r = ( m v ) / ( |q| B)

• a particle in w/ v_initial at an angle will move in a helical path

Magnetic Force of Current-Carrying Wire

F_mag = ILBsinθ

• F_mag perpendicular to I

Right hand rule for F_mag, I, B

Two vertical sides of current-carrying wires

• right side force is going out of page, left side force is going into page

• On vertical sides: Forces are equal in magnitude, but opposite in direction

• Creates torque

Torque on current carrying loop

𝜏 = NIABsinθ

• A = area, N = # of turns/loops

• torque increases as # of loops increases (N), if current ( I ) increases

Direction of magnetic field due to Current carrying wire right hand rule

Ampere’s Law

∑BΔL = μ_o I_enclosed

μ_o = 1.26 × 10^-6

Ampere’s Law to solve for B

B = (μ_oI) / (2πr)

• 2πr is circumference

Currents in same direction

• forces come towards each other

• magnetic field in opposite directions (both going CW or CCW)

Currents in opposite direction

• forces go away from each other

• magnetic field in same directions (one going CW other going CCW)

F_mag equation for two current-carrying wires

F_mag = (μ_oI₁I₂) / (2πd)

• d = 2 * circumference

Magnetic Field of a Current Loop / Bar Magnet (B_loop)

B_loop = (Nμ_oI) / (2R)

Magentic Field of a solenoid (B_solenoid)

B_solenoid = (Nμ_oI) / L = μ_onI

• n = # of turns / unit length (N/L)