Algorithm to find magnetic force on a particle with charge q placed into magnetic
field B
Formula: F=q[vB]
1. Locate the plane which is made of vectors v and B, vector product [vB] is a vector
perpendicular to the plane. However note that we have two possible orientations!
2. To fix the orientation, orient your right hand perpendicular to the plane and try to
rotate vector v towards vector B by a shortest angle. If this is possible, the
orientation of your right hand (which stands perpendicular to the plane) is the
result of the vector product. If not, vector product is in the opposite direction.
Confirm that by reorienting your right hand in the opposite direction and repeat
the procedure.
3. To find the force, the vector product [vB] has to be multiplied by the charge of the
particle. Since there are positive and negative particles, we can multiply [vB]
either by positive number or negative. If the charge of the particle is “+” force is
in the the direction as [vB], if charge of the particle is “-“ force is in the opposite
direction.
Algorithm to find magnetic force on a current carrying wire placed inside the
magnetic field B
Formula F=i[LB]
The algorithm is exactly the same as above. Since the direction of the current is assumed
to be given by the movement of the positive charge through the wire, vector L describing
the length of the wire is directed along the current.
1. Choose the direction of vector L along the current.
2. Locate the plane which is made of vectors L and B.
3. To fix the orientation of the vector product [LB] use the right-hand rule:
Orient your right hand perpendicular to the plane, try to rotate L towards B by
shortest angle. If you succeed, orientation of your right hand gives the result
of the vector product, if not, vector product is in the opposite direction.
4. The direction of the force is the same as the direction for the vector product,
since i is assumed to be positive here.
Algorithm to find the magnetic field due to straight long wire.
Formula for the value of the field: B=0i/2R
1. Orient your large finger along the current
2. Partially fold your four other fingers. The direction of your 4 folded fingers will
show the direction of the field anywhere in the circle around the wire.
Algorithm to find the magnetic field due to circular arc of wire.
Formula for the value of the field: B=0i/4R which for a full circle is reduced to
B=0i/2R. To find the direction of the field inside the circle, the algorithm for the straight
wire can be used. However you can find another useful algorithm:
1. Orient your right hand perpendicular to the plane which is made of the
arc(circle).
2. Simulate the motion of the current flow by your right hand. If you succeed,
the orientation of your right hand shows the direction of the magnetic field in
insider area of the cirrle (at the center of the arc). If you did not succeed,
reorient your right hand in the opposite direction and repeat the procedure.
One more algorithm can be used too:
1. Fold your four fingers to simulate the shape of the arc (circle) and orient them
along the current flow.
2. Straighten your large finger, so that it gets perpendicular to the plane of the arc
(circle): it will show the direction of the magnetic field in the insider area of the
circle (at the center of the arc)
Rules for magnetic force between two parallel current carrying wires
F=0LI1I2d
1. If two currents are in parallel, the two wires attract each other.
2. If two currents are antiparallel, the two wires repel each other.
Algorithm to find the direction of the induced current in the Faraday law.
Induced EMF E inside the wire frame (loop, turn, etc) placed into magnetic field so that
the flux of magnetic field  through the frame changes with time is given by
E=-d/dt
In particular situation when we change the magnetic field with time, E=-AdB/dt, and the
induced EMF is determined according to vector dB/dt. The following algorithm can be
used.
1. Understand the direction of vector dB/dt. In cases when the magnetic field
increases with time, dB/dt is along the field. In cases when the magnetic field
decreases with time, the vector dB/dt is opposite to the field. In general, simply
differentiate the vector B(t) and understand the direction of dB/dt
2. Once found the direction of dB/dt, place the induced magnetic field vector Bind in
the direction opposite to dB/dt.
3. Choose the direction of the induced current in the frame (loop, turn, etc) to
simulate the direction of the induced magnetic field Bind.