The fundamental nature of the Electric and Magnetic (E&M) interaction will be discussed with emphasis on the material for which students will be responsible.

There are four fundamental forces or interactions:

- gravity,
- E&M,
- weak (very minor impact on everyday life) and
- strong (nuclear force)

The E&M interaction keeps electrons orbiting the nucleus which makes this interaction the primary ingredient in the behavior of atoms and therefore leads to material properties and the typical behaviors experienced in our world. From pounding in a nail to lighting a street corner, from mixing ingredients for bread to designing proteins, from building a bridge to support the weight of cars to transmitting text message, throughout biology and chemistry the forces that push and hold charges in place plays the dominant role in determining outcomes. Although it is clear that E&M plays this role, the complexity of the various systems discussed require the approach taken in many areas of science. They handle the manifestations of the E&M interaction rather than a direct reliance on first principles calculations. Chemistry is a science that guides our understanding of atomic and molecular processes. These processes can be understood and predictions made in terms of reaction rates, the shell model etc. Electrical engineering uses circuit elements (resistors, wires, power supplies, amplifiers) to understand circuits. And of course biology doesnÕt attempt to understand the human body by addressing the motion of the electrons and protons in our bodies (cells, genetics, muscle tissueÉ). The underlying theory (E&M) is known and well understood but the complexity of the systems of interest warrant the development of other techniques and models. So we look at the fundamentals appreciating their importance while realizing that for many applications other approaches will be used in analysis.

What are the basic relationships for E&M

- Electric charge exists and charges can be isolated and their interaction studied.
- two types ¸ + positive , - negative
- like repel, unlike attract
- fundamental particles posses multiples of some basic amount.

i. The charge on every electron is exactly the same 1.6 e-19 C

- The force between two charges can be expressed as CoulombÕ law in terms of the charges , the distance , and the direction determined by the line joining the charges .

Qualitative and
quantitative understanding is required for this equation. |

Force acts along the
line joining the charges. Force is repulsive (¸+ pos.), attractive (¸- neg.) Force decreases with
the distance between the charges, increases when closer Students should be
able to calculate the magnitude and direction of the force between two
charges using the formula. |

- APPARENT magnetic poles ¸ N, S

N,S
poles |

Since no magnetic
monopoles i.e. isolated, separate N or S poles have been found, E&M
includes these entities as apparent poles. The N and S poles must be generated by
electric charges. As discussed below an electric current will produce a bar
magnet (magnetic dipole). This affords and interesting opportunity. The
nature of N,S poles can be ascertained. The
properties of these non existent entities can be
deemed and used to help understand the magnetic interaction even if we know
that they are not real. |

- Two types N,S
- like repel unlike attract
- weakens as distance between poles increases
- have the same force behavior as electric charge. [Students need to understand the qualitative nature of this force but no calculation of the force between poles will be required.]

Given the forces, electric and magnetic, described above it becomes important to separate the force so that one can examine the possibility for interaction due to a set of isolated charges and the actual force when a new charge is placed in the vicinity. This leads to the notion of electric and magnetic fields. One finds the force per unit charge surrounding any distribution of electric or magnetic charges. The usefulness of this approach is perhaps initially confusing but the idea that fields fill the space around a charge has become a central element in E&M theory. Students will therefore be required to understand the basic idea of fields. Since the electric field is perhaps the most straightforward we will use it as the basis for our understanding and then ascribe to magnetic fields a similar behavior.

electric field is the force/unit charge

To determine the field at any point in space we first find the force that a test charge would experience at this point. Since we use SI units we could ask what force is experienced by 1C of charge. This is the value for in N/C. Obviously if we were to choose a test charge of 2C the force would be twice as large but since the field is defined as force per unit charge we need to divide by the 2C of the test charge and the field value at that point is the same independent of the test charge. One could carry out this process at every point in space. The field around charges (static, not moving) is defined everywhere and knowing the force law (Coulombs law) the value for the field can in principle be calculated for every charge distribution.

An electric field fills all of space due to the distribution of static (not moving) charges. The field provides the magnitude and direction of the force that would be experienced by a charge Q. ¸

Similarly we can imagine magnetic fields that fill space. These fields inform us of the force that an apparent N or S pole would feel at a point in the field.

- E&M adds additional ways that the electric fields can be created. Changing magnetic fields can additionally generate an electric field. This new way to generate the field doesnÕt change its impact. Electric charge Q will feel the force of a field as no matter how that field is generated. So we have simply added a new way to generate the field but not modified how we understand the effect on charges.

- E&M adds additional ways the magnetic field can be generated. Here we have two pieces.
- Electric current produces magnetic fields.
- Changing electric fields produce magnetic fields. {As stated in class while this was a critical point in finalizing the understanding of E&M, it doesnÕt impact many of the applications based on E&M.}

If there are
electric currents why not magnetic currents? |

Since no N,S poles actually exist all magnetic fields are generated by
moving charge or changing electric fields. Although it is useful to imagine
the existence of these poles to define the magnetic field, the lack of their
discovery prohibits the theory from directly requiring these poles or to use
these poles directly. A magnetic
analog for electric current would require separated N or S poles in
motion. It is impossible to
create this scenario using electric currents because when an apparent N-pole
is generated by an electric current an accompanying apparent S-pole is generated. Moving the electric current then moves
both N and S together so there is no overall transport of magnetic
poles. When you move equal
amounts of positive and negative charge together the resulting electric
current is also zero. We can use
N,S poles to help us imagine what a magnetic field
is but we canÕt incorporate them as a way to generate fields. |

The fields generated by these additional mechanisms are more complicated to determine. Students are not responsible for the general relationship between electric currents and the generated magnetic fields or between changing electric and magnetic fields and the generated magnetic and electric fields. Students need to know what can create a field but not necessarily the details of the created field.

Special cases ¸ Students do need to know the field configuration for the following special cases:

- Isolated charge
- Pair of equal and opposite charges or poles separated by a short distance (electric dipole, magnetic dipole[bar magnet]
- Magnetic field of a straight wire
- Magnetic field of a loop or tightly wound coil.

(See lect15 week 9 for these examples)

Normally the field configuration is represented by field lines. The lines informs of both the magnitude and the direction of the field. The field is tangent to the line and is directed based on the arrows shown. The magnitude is related to the number of field lines in the vicinity. For example, the lines become more tightly packed the closer you get to the charge and the field increases as you approach a charge. A positive charge would be repelled in the radial direction as indicated by the outward going radial field.

- To complete the picture we need to add the interaction between electric charge and magnetic field. The complete force law is

.

This shows that charges at rest do not experience magnetic forces but moving charges do feel magnetic forces if they move in a magnetic field. Students will not be expected to apply the formula as it is written above. Students should recognize that the force on a moving charge is always perpendicular to both the velocity and the field and that no magnetic force is felt if the charge is moving parallel to the magnetic field. This is a different behavior than forces that have been addressed up to now. Students should recognize this and be able to explain the direction of the force knowing the velocity and the field orientation.