handbook of modern sensors

3.3 Magnetism 53
electric charge can be deflected as a result of its interaction with the magnetic field
is a fundamental in electromagnetic theory. Deflected electric charges result in an
electric field generation, which, in turn, leads to a voltage difference in a conducting
material, thus producing an electric current.
The intensity of a magnetic field at any particular point is defined by a vector B,
which is tangent to a magnetic field line at that point. For a better visual representation,
the number of field lines per unit cross-sectional area (perpendicular to the lines) is
proportional to the magnitude of B. Where the lines are close together, B is large, and
where they are far apart, B is small.
The flux of magnetic field can be defined as
∮
B = B ds, (3.28)
where the integral is taken over the surface for which F B is defined.
To define the magnetic field vector B, we use a laboratory procedure where a
positive electric charge q 0 is used as a test object. The charge is projected through the
magnetic field with velocity V.Asideways deflecting force F B acts on the charge (Fig.
3.13A). By “sideways,” we mean that F B is at a right angle to V. It is interesting to
note that the vector V changes its direction while moving through the magnetic field.
This results in a spiral rather than parabolic motion of the charge (Fig. 3.13B). The
spiral movement is a cause for a magnetoresistive effect which forms a foundation for
the magnetoresistive sensors. The deflecting force F B is proportional to the charge,
velocity, and magnetic field:
F B = q 0 VB. (3.29)
The vector F B is always at right angles to the plane formed by V and B and, thus,
is always at right angles to v and to B, that is why it is called a sideways force. The
magnitude of magnetic deflecting force according to the rules for vector products is
F B = q 0 vB sin φ, (3.30)
where φ is the angle between vectors V and B. The magnetic force vanishes
if V is parallel to B. Equation (3.30) is used for the definition of the magnetic
(A)
(B)
Fig. 3.13. Positive charge projected through a magnetic field is subjected to a sideways force
(A); spiral movement of an electric charge in a magnetic field (B).