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Magnetostatics
Magnets and Magnetic Fields
Magnets have two ends – poles – called north and
south.
Like poles repel; unlike poles attract.
Magnetic fields ( B )can be visualized using magnetic
field lines, which are always closed loops.
Magnetic fields is tangential to the field
lines.
The field is strongest where the field
lines are most dense
F = qv x B
The field is strongest where the field
lines are most dense
SI units N/(C·m/s) = tesla (T)
Force on Electric Charge Moving in a Magnetic
Field
The force on a moving charge is related to the
force on a current:
F = qvBsinθ
Once again, the
direction is given by a
right-hand rule.
Force on Electric Charge Moving in a
Magnetic Field
If a charged particle is
moving perpendicular
to a uniform magnetic
field, its path will be a
circle.
The magnetic force is
supplying the centripetal
force
qvB = mv2/R  R = mv/qB
Electric Currents Produce Magnetic Fields
Experiment shows that an electric current
produces a magnetic field.
Force on Electric Charge Moving in a
Magnetic Field
Problem solving: Magnetic fields – things to
remember
1. The magnetic force is perpendicular to the
magnetic field direction.
2. The right-hand rule is useful for determining
directions.
3. Equations in this chapter give magnitudes
only. The right-hand rule gives the direction.
Force on Electric Charge Moving in a
Magnetic Field
Magnetic on a Current –Carrying Wire
The total force on a wire segment will be
F = N (qvB)
N charges travel through the segment in time t = l/v
The current can be written as
I = q/t = Nq/(l/v) = Nqv/l F = IlB
The force on the wire depends on the
current, the length of the wire, the magnetic
field, and its orientation.
F = IlBsinθ
This equation defines the magnetic field B.
Consider a rectangular loop of wire with dimension
l and w, carrying current i as shown in figure (a).
The net torque about the central axis of the loop
will be
A = area of loop
Magnetic Field due to a Long Wire
The field lines created on a
long wire form concentric
circles on the wire.
Long wire rule: Place the thumb of your
right hand in the direction of the current.
Your fingers will wrap in the direction of
the field line circulation.
The field is inversely proportional to the distance
from the wire:
B = k’ I/R
The constant k’ has the value:
k’ = 2 x 10-7 T•m/A
Force between Two Parallel Wires
The magnetic field produced at the
position of wire 2 due to the
current in wire 1 is:
B = k’ I1/d
The force this field exerts on a
length l2 of wire 2 is:
F = l2 (k’ I1I2/d)
20.6 Force between Two Parallel Wires
Parallel currents attract; antiparallel currents
repel.
Key Formulas
F = qv x B
F = qvBsinθ
R = mv/qB
F = IlBsinθ
net t = iAB sinθ
B = k’ I/R
F = l2 (k’ I1I2/d)