Phy 213: General Physics III Chapter 28: Magnetic Fields Lecture Notes

N S The movement of electric charge produces a magnetic (B) field A single magnetic point charge (called a magnetic monopole) has never been discovered in nature Magnetism always exists as a dipole never as a point “charge” Magnetic materials have both north and south poles Magnetic field lines point from North (N) to South (S) The units of magnetic field are called Tesla (T) 1 Tesla (T) = 1 N. s/C. m Magnetic Fields

The Earth as a Magnet –The geographic “North Pole” is really the South pole of the magnetic field –The geographic “South Pole” is really the North pole of the magnetic field Although its value varies depending on location, the magnitude of the Earth’s magnetic field is ~ 6x10 -5 T The Earth has a magnetic field and acts like a big magnet We define the magnetic “north” direction as the direction the North end of a compass points

Magnetic Fields (moving charges) Moving charges produce magnetic fields The magnitude of the produced magnetic field depends: –Magnitude of charge (q) –Speed of the charge (v) –Distance from charge (r) Direction of magnetic field is determined by the “right hand rule” –Point thumb in direction of v (or –v for negative charge) –Curl fingers around the thumb –The direction of the fingers is the direction of magnetic field Examples: What is the direction of the B field? + v - v

Magnetic Force Magnetic fields exert force on moving charges (the magnetic force) The direction of the magnetic force is –Perpendicular to the direction of movement –Perpendicular to the direction of magnetic field The magnetic force exerted on a charge depends on: –The magnitude of the moving charge (q) –The speed of the moving charge (v) –The magnitude of the magnetic field (B) –The angle (  ) between v and B To calculate magnetic force on a moving charge: or

Magnetic Force on a Current-Carrying Wire Current carrying wires have moving charge When placed in a magnetic field, the field can exert a force on these moving charges The magnetic force vector exerted on a current carrying wire of length, L, is: The magnitude of the magnetic force vector: Example: i

The Hall Effect When a perpendicular magnetic field is applied to a current carrying material, the charge path becomes curved with moving charge accumulating on one face of the material & equal and opposite charges exposed on the other face. The separation of charge establishes an electric field that opposes the migration of further charge, and an electrical potential builds up for as long as the current is flowing. V Hall i B + - e-e-

Torque Exerted on a Current Loops Although the net magnetic force exerted on a current carrying loop in a magnetic field is zero, the field does exert torque on the loop Consider a square loop (length of sides = L and current = i) in a constant magnetic field: On 2 sides of the loop, F B =0 For each of the other sides, F B = iLB is pointing opposite directions Each of these forces exerts a torque on the loop: The net torque on the loop is: When there are N loops: i

Magnetic Moment The quantity NiA is referred to as the magnetic moment vector (  ) for the loop The direction of is the normal vector to the face of the loop: The torque on the loop can then be expressed (for any N, A, and i) as: i The magnetic potential energy is given by:

Magnetic Force in DC Motors A simple DC motor is comprised of a rotating wire coil (called an armature) connected to a battery (or DC power source) The armature is placed within a between the opposite poles of 2 magnets As current passes along the coil, the magnetic field exerts force on the wires generating torque that results in the rotation of the armature As it rotates, the magnitude of torque (force) acting on the armature depends on its orientation in the magnetic field