Unit 4 Day 7: Magnetic Fields due to Wires

• Magnetic Field in a Straight Wire

• Magnetic Fields in 2 Parallel Conducting Wires, Side by Side

• Magnetic Forces Between Parallel Wires

Magnetic Field in a Straight Wire• In a straight, current carrying conductor,

there exists a magnetic field around the wire, proportional to the current

r is the radial distance from the conductor

AmTwhere

r

IB

70

0

104

2

Two Current Carrying Conductors Side by Side

• If there are two current carrying conductors side by side, but the current is going in the opposite directions, then the total magnetic field will have a magnitude of:

21 BBBTotal

Magnetic Force Between Parallel Wires• We know that when a current carrying conductor is in the

presence of a magnetic field, it feels a force exerted by that field.

Magnetic Force Between Parallel Wires• The force that wire #2 sees is due to the

magnetic field generated by wire #1, separated by distance d

• Similarly, wire #1 sees a force due to the magnetic field of wire #2 (Newton’s 3rd Law)

d

lIIF

d

IBbut

BlIF

2

2

22102

101

1222

d

lIIF

2

12101

Magnetic Forces Between Parallel Wires

• Parallel currents in the same direction exert an attractive magnetic force on each other

• Parallel currents in the opposite direction exert a repulsive force on each other

• It can be shown from Newton’s 3rd Law, that the magnetic force produced by I2 exerts an equal but opposite force on I1