Almost all undergraduate physics curricula start with one term studying mechanics. In the first term, students learn about motion and the forces that cause motion. Then they learn a (different) way of explaining motion in terms of energy conservation. The second physics term is spent studying electricity and magnetism. Students learn about the motion of charged particles and the forces that cause that motion. Then they learn a (different) way of explaining motion of charges in terms of energy conservation. There seems to be a nice sort of symmetry between the two courses, but I encounter a problem each year, namely, my Electricity and Magnetism students have a hard time applying the skills they learned in Mechanics to Electricity and Magnetism. I’m sure that one culprit is time; the students have probably forgotten what they had learned before. But I’m wondering if part of the problem is the lack of a unified approach to representing physical situations in their first physics course. The students spend a little time learning how to use Newton’s Laws, then a little time with Conservation of Momentum (which is sometimes presented as a separate topic when in fact it easily combines with Newton’s Laws), then a little time learning about Conservation of Energy. From a student’s perspective, I wouldn’t be surprised if his or her Mechanics class felt like this:

- There are quantities called position, velocity, acceleration, and time — sometimes you have to use kinematic equations to answer questions
- There are these things called forces — sometimes you have to use force equations to answer questions
- There is this thing called momentum — sometimes you have to use momentum equations to answer questions
- There is this thing called energy — sometimes you have to use energy equations to answer questions

The students don’t have to think too much about which physical principles (i.e. Newton’s Laws, Conservation of Momentum, or Conservation of Energy) to apply in order to answer a question because the questions that are asked are pretty much always aligned with the current chapter. It should be no surprise, then, when students have difficulty knowing which physical principle to apply to a generic situation. In fact, when presented with a generic situation, the solutions that I see from students are often “Equation Soup”.

**Equation Soup**

noun

1. A collection of partially-worked formulas from the Equation Sheet that have letters in them that correspond to the quantities that were given in the problem statement

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**The problem is perpetuated in the Electricity and Magnetism course because the curriculum goes through exactly the same process, except now it gets applied to the property of charge instead of the property of mass.

What if, instead, the courses were organized as follows:

**First Course – Interactions as Forces**

- Objects and systems have properties such as mass and charge.
- Interactions between objects can be described by forces.
- the gravitational force is an interaction between two objects with mass
- the electric force is an interaction between two objects with charge
- the magnetic force is an interaction between two objects with charge that are moving

- Knowledge of the forces acting on a system can be used to describe the motion of the system.

**Second Course – Interactions as Energy
**

- Objects and systems have properties such as mass and charge.
- Interactions between objects can be described using energy.
- gravitational potential energy is the energy of interaction between two objects with mass
- electric potential energy is the energy of interaction between two objects with charge

- Knowledge of the energy transfers within a system can be used to describe the motion of the system.

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**In this course curriculum, the different subtopics in each course are the types of interactions (i.e. gravitational, electric, or magnetic), not how you choose to represent those interactions (i.e. forces or energy). For example, in the Interactions as Forces course, you learn that the Earth interacts with all other massive objects (i.e. moon, other planets, the sun), you represent all of those interactions with an arrow called a “force”, then you apply the rules of forces to determine the resulting motion of the Earth. Next you learn that a charged particle interacts with all other charged particles, you represent all of those interactions with an arrow called a “force”, then you apply the rules of forces to determine the resulting motion of the charged particle. The same goes for the magnetic force and every situation that is a combination of the gravitational force, the electric force, and the magnetic force. In the Interactions as Energy course, you take exactly the same situations as before, except now you represent those interactions with a scalar quantity called “potential energy”, then you apply the rules of energy transfer to determine the resulting motion of the object. The process of how to represent and analyze a situation is always going to be the same for every type of interaction. In terms of teaching, the advantage of this is that the students will get practice in applying the same process over and over again, and they should eventually start to see that any interaction can be represented either with forces or energy. The choice of which representation to use comes down to ease and efficiency. The other advantage here is that rather than promoting the idea that there is the “mechanical world” and the “electromagnetic world”, there is only one world, and we choose to represent it in whatever way is most convenient.

I’m sure this has been considered before; in fact, I remember reading somewhere about some schools that actually do separate their courses this way. Is there a compelling reason that I am missing for why the vast majority of curricula are divided into Mechanics and E&M instead?