Magnetic Forces and Fields

Question 1

Magnetic Force on Moving Charge

Answer 1

• Particle with charge q moving with velocity v through a magnetic field B, will experience a magnetic force, F_B, with magnitude
  
  • F_B= |q|vBsinθ
    
    • θ is the angle between v and B
      
      • If the charge is at rest (v= 0) then F_B= 0 as magnetic forces only act on moving charges
      • If v is parallel (or antiparallel) to B, then F_B= 0 as in both cases sinθ= 0
        
        • Only charges that cut across the magnetic field lines will experince a magnetic force
      • Magnetic force is maximized when v is perpendicular to B, since if θ= 90^o, then sinθ is equal to 1 its maximum value
      • The direction of F_B is always perpendicular to both v and B and depends on the sign of the charge q
• SI Unit for the magnetic field is the tesla (abbrev. T): 1 N/(A•m)
  • Also common unit is gauss (abbrev. G): 1 G= 10^-4 T

Question 2

Right-Hand Rule

Answer 2

• Right hand, palm up- point thumb in direction of V and fingers in the direction of B
  
  • If q is positive, F_B points out of the palm
  • If q is negative, F_B points into the palm
    *

Question 3

Magnetic Force vs. Electric Force

Answer 3

• A magnetic force acts on a charge only if the charge is moving
  
  • The electric force acts on a charge whether it moves or not
• The direction of the magnetic force is always perpendicular to the magnetic field, while the electric force is always parallel (or antiparallel) to the electric field

Question 4

Magnetic Force on Current-Carrying Wire

Answer 4

• As magnetic fields affect moving charges, they should also affect current-carrying wires (wire that contains a current contains charges that move)
  
  • Wire of length l immersed in magnetic field B, carrying current I; magnitude of the magnetic force it feels is:
    
    • F_B= I_currentl_lengthsinθ
      
      • I and l, (i and L contain subscript due to similar appearnce)
      • θ is angle between length and B, direction of length is the direction of the current, I
      • Direction of F_B given by the right-hand rule
      • Direction of current is the direction that positive charges would flow

Question 5

Magnetic Field Created by Current-Carrying Wire

Answer 5

• Source of magnetic fields are electric charges that move (e.g. spin, circulate, move through space, or flow down a wire)
  
  • Wire with current I generates a magnetic field in the surrounding space that’s proportional to I and inversely proportional to r, the distance from the wire
    
    • B∝ I/r
      
      • Magnetic field lines are usually circles with centers on the wire
        
        • Direction of circles is determined by variation of the right-hand rule
          
          • Grab wire with right hand with thumb pointing in direction of current: the direction in which fingers curl around the wire gives direction of the magnetic field lines