Force between two Current Carrying Wires
- Consider two wires, each carrying current in the same direction
- Find the force on wire 2 due to presence of wire 1
- Find the field due to current in wire 1 at the location of
wire 2.
- Magnitude
- Direction
- into page at location of wire 2
- Find the force on a current carrying wire due to this magnetic field
- the field and current are perpendicular to each other
- this is frequently written as a force per unit length
- The direction of the force may be found by applying the right hand
rule
- Force will be to the left
- Verification of Newton's Third Law
- Find the force on wire 1 due to presence of wire 2
- Find the field due to current in wire 2 at the location of wire 1.
- Magnitude
- Direction
- out of the page at the location of wire 1
- Find the force on a current carrying wire due to this magnetic field
- the field and current are perpendicular to each other
- this is frequently written as a force per unit length
- The direction of the force may be found by applying the right hand
rule
- Force will be to the right
- Two parallel currents will exert an attractive force on each other; two anti-parallel
currents will exert a repulsive force on each other.
- Ampere's Law
- Similar to Gauss's Law in that we try and take advantage of symmetry to calculate
the magnetic field.
- try to find a path where the scalar product of the magnetic field with the
path is constant
- Magnetic Field of a long straight wire (inside and outside)
- outside
- by symmetry we'd expect the field to form circular loops centered
around the wire, if we pick a circular loop for our Amperian loop,
then the scalar product of the magnetic field will be constant
- If we are outside of the wire, then all of the current flows through
the loop
- inside
- by symmetry we still expect the field to form circular loops
centered around the wire, if we pick a circular loop for our
Amperian loop, then the scalar product of the magnetic field will
be constant
- Because we are inside the wire, only a fraction of the total current
will pass through the loop.
- Magnetic Field of a Solenoid
