Conceptual Notion of Fields Lesson Plan

🔖 Topics

• Scalar fields
• Vector fields
• Higher-order (tensor) fields
• Time independent vs. time dependent fields
• Linear fields
• Superposition

🎯 Objectives

• Describe the properties of a field
• Explain why we need the idea of fields in the study of physics
• Calculate the properties of a scalar field at a given point in space
• Calculate the properties of a vector field at a given point in space
• Calculate the net result of two or more combined fields at a given point in space

📋 Sequence

• 🟢 Definition of a field in physics
• 🟢 Scalar fields (e.g. temperature)
• 🟢 Vector fields (e.g. wind velocity)
• 🟢 Higher-order (tensor) fields (e.g. stress and strain in materials)
• 🟢 Time independent vs. time dependent fields
• 🟢 Linear fields
• 🟢 Superposition

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

1. A vector field is given by the equation $\vec{A}=(20y)\hat{x}-(30x)\hat{y}$. Vector field B is given by the equation $\vec{B}=5\hat{x}-(10y)\hat{y}$. What is the value of the field at the point (1,1)?
2. Sketch the gravitational field around the planet Earth when you are zoomed out on a planetary scale.
3. Sketch the approximate gravitational field near the surface of the Earth (this is the assumption we made for most the first course in introductory physics).
4. What is an example of a scalar field? You can’t use the examples that I gave in class!
5. What is an example of a vector field? You can’t use the examples that I gave in class!
6. Although we won’t deal with them in this class, can you think of an example of a higher-order (tensor) field? You can’t use the examples that I gave in class!

✅ Partial Solutions

1. $(25,-40)$

📘 Connected Resources

N/A