1. Magnetic Fields due to Current in a Wire

2. A Surprising Discovery
In 1820, Hans Christian Oersted discovered that moving charges create a magnetic field.

3. Magnetic Field of a Current Carrying Wire
Hans Christian Oersted discovered that a wire carrying current influenced the needles of nearby compasses.
By applying right-hand-rule #2, the direction of the magnetic field can be determined around the wire.
For an infinitely long straight wire:
B is proportional to I and inversely
proportional to r.
Magnetic Field due to a wire. I r
B a

4. Magnetic Force on Current Carrying Wires
When two current carrying wires have current flowing in the same direction, they will be attracted to one another (a).
When two current carrying wires have current flowing in opposite directions, they will repel (b). F
(a) F
(b)

5. Magnetic Force on Current Carrying Wires(cont.)
-The influence of the magnetic field of wire (a) on wire (b).
-Using RHR #1, we see that the force by wire (a) on wire (b) is such that it is attracted to wire (b).
-The same is true for wire (b) on wire (a).
-However, even if the current is flowing in opposite directions, won’t the conductors be attracted to one another? x
(a)
(b) x x B

6. Magnetic Force on Current Carrying Wires(cont.)
                              
-No. Note that the magnetic fields cancel each other between the conductors while they add outside for two parallel conductors with current moving in the same direction.
-As a result the conductors are attracted to one another.
-In the case where the conductors have current flowing in opposite directions, the field lines add between them while they cancel outside. This results in a net repulsion between the two conductors.

7. Magnetic Field in a Loop of Wire
For the center of a circular loop, the magnetic field is:
Where:
N = number of turns of wire.
R = Radius of loop. NI R
B a

8. Magnetic Field of a Solenoid
For a solenoid, the magnetic field is given by:
B a NI L
B a nI
Where:
n = the number of turns per length of coil = N/L L

9. Key Ideas
The strength of a magnetic field created by current in a wire is inversely proportional to the distance from the wire.
Two current carrying wires will attract each other if the current flows in the same direction
Two current carrying wires will repel each other if the current is in opposite directions.
The strength of the magnetic field of current in a loop is proportional the current in the loop and the number of loops.