Magnetism Tip Sheet
The study of magnetism generally requires a vector approach. For this reason, we will
only look at magnetic fields (a vector property of space) and magnetic forces (a vector
interaction). While there is a scalar approach, it requires mathematics beyond the
requirements of this course.
Magnetic Fields
Moving, charged particles create magnetic fields. Here is a table of formulas for some
specific cases:
Source
Field Magnitude
B = μ0qv*sinθ/r2
μ0 = 4πE-7 Tm/A
q = charge
v = speed
r = distance between charged
particle and point in space
θ = angle between velocity
vector and a vector pointing
from the charged particle to the
point in space
Long (L >> r) current-carrying B = μ0I/(2πr)
wire (or stream of charged
I = current
particles)
r = distance between wire and
point in space
Loop or loops (R >>
B = μ0NI/(2R)
thickness of loop); at center R = radius of loop
N = number of loops
Loop or loops; on axis going B = μ0NIR2/[2(z2 + R2)3/2]
through loop, perpendicular z = distance from center of loop
to loop
Solenoid (L >> R); near
B = μ0NI/L
center, inside solenoid
L = length of solenoid
Moving, charged particle
Field Direction (RightHand Rule)
Thumb = velocity
Fingers curl = field
Note: reverse the
direction for
negatively charged
particle
Thumb = current
Fingers curl = field
Fingers curl = current
Thumb = field
Fingers curl = current
Thumb = field
Fingers curl = current
Thumb = field
Magnetic Forces
Moving, charged particles within a magnetic field can experience a force. Here is a table
of formulas for some specific cases:
Receiver of Force Magnitude of Force
Moving, charged F = qvB*sinθ
particle
q = magnitude of charge
v = speed
B = magnitude of magnetic
field
θ = angle between velocity
vector and magnetic field
vector
Current-carrying
wire
F = ILB*sinθ
I = current
L = length of wire
θ = angle between direction
of current and direction of
magnetic field
Force Direction (Right-Hand Rule)
Thumb = velocity
Index finger = magnetic field
Fingers bend = force
OR
Thumb = force
Index finger = velocity
Fingers bend = magnetic field
Note: Reverse a vector or use left
hand for negatively charged particles
Thumb = current
Index finger = magnetic field
Fingers bend = force
OR
Thumb = force
Index finger = velocity
Fingers bend = magnetic field
Magnetic Torque
A current-carrying loop in a uniform magnetic field has zero net force, but does have a
net torque:
τ = IAB*sinθ
A = area
θ = angle between external field and field generated by loop
The direction of the torque will be so that the magnetic field of the loop attempts to line
up with the external magnetic field.