Currents and Magnetic Fields

• Hall Effect
• Magnetic Field into Screen
• positive charges to left
• right hand rule
• positive charges deflected down
• bottom at higher potential than top
• negative charges to right
• right hand rule
• negative charges deflected down
• top at higher potential than bottom
• Hall Voltage
• F_m = qvB
• magnetic force on moving charge
• F_e = qE
• electric force on charge
• F_e = F_m
• equilibrium
• qvB = qV/d
• vB = V/d
• Hall Voltage = > V=vBd



• Magnetic Force on a Current
• Many Charges ==> Current
• Total Force on segment:
• length = l
• area = A
• Force on one charge => F = qv_d x B
• F_t = (qv_d x B)N
• N is total number of charges
• Total Force:
• N= n Al
• n = charges/volume
• Al = volume
• F_t = (qv_d x B) n Al
• Remember: I = nv_dAq
• F_t = I l x B
• the magnitude of the force
• F_t = BILsinq
• If the segment is not straight and the magnetic field is not uniform
• the force on a short segment
• 
• the total force on the wire

• Examples

• Torque on Loop
• Forces on loop
• top: F = 0
• I parallel to B
• bottom: F = 0
• I parallel to B
• left side: F = Bib
• out of page
• right side: F = Bib
• into page
• zero net force
• Torque on Loop
• Loop will feel torque
• t₁ = F₁r₁ = BIb a/2
• t₂ = F₂r₂ = BIb a/2
• t= t₁ + t₂
• t = (BIb a/2) x 2
• t= BIba = BIA or BIA sinq
• Define the magnetic moment of the current loop
• 
• the torque can be written
• 
• Application
• Galvanometer
• Examples
• Motion of Charged Particles
• Force always perpendicular to v
• circular motion
• F = qvB = mv²/r
• r = mv/qB
• isotope separator