Ch 29 Magnetic Fields Due to Currents
Vacuum permeability constant:
.
3 Force Between Two Parallel Currents. To find the force on a current-carrying wire due to a second
current-carrying wire, first find the field due to the second wire at the site of the first wire. Then find the
force on the firsts wire due to that field. If two parallel wires with currents and , the force on a wire
segment of length , due to the other wire, is
, where is the distance between
the wires. Parallel currents attract each other, and antiparallel currents repel each other.

Checkpoint 1
4 Ampere’s Law. ∮ ⃗ ⃗⃗⃗⃗
.
The integral runs over a closed loop. The current
runs through a surface bounded by the loop. Curl
your right hand around the Amperian loop, with the fingers pointing in the direction of integration. A
current through the loop in the general direction of your outstretched thumb is assigned a plus sign, and
a current generally in the opposite direction is assigned a minus sign.
Magnetic field outside/inside a long straight wire with current: If
distance from the wire center, then
 outside the wire (
 inside the wire (


) the field is
) the field is
is the wire radius, and is the
, while
( )
.
Checkpoint 2
Sample Problem: Ampere’s Law to find the field inside a long cylinder of current
5 Solenoids and Toroids.
Magnetic field of a solenoid: Outside the solenoid this is very weak. Inside it is
number of turns per unit length in the solenoid.
Magnetic field of a toroid: Outside the toroid this is very weak. Inside it is
the total number of turns, and is the distance from the center of the toroid.

, where
( )
is the
, where
is
Sample Problem: The field inside a solenoid (a long coil of current)
6 A Current-Carrying Coil as a Magnetic Dipole.
Magnetic field of a coil: For points along the axis far from the loop, this is ⃗
distance and is the coil’s dipole moment, with
.

( )
Checkpoint 3
----------------Material below is not covered in this course----------------------------------------------------2 Calculating the Magnetic Field Due to a Current
, where is the