• Use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to describe and predict the gravitational and electrostatic forces between objects. (HS-PS2-4)

• The structure and interactions of matter at the bulk scale are determined by electrical forces within and between atoms. (9-12)

• Forces at a distance are explained by fields (gravitational, electric, and magnetic) permeating space that can transfer energy through space. Magnets or electric currents cause magnetic fields; electric charges or changing magnetic fields cause electric fields. (9-12)

• When two objects interacting through a field change relative position, the energy stored in the field is changed. (9-12)

• Different patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena. (9-12)

• Cause and effect relationships can be suggested and predicted for complex natural and human designed systems by examining what is known about smaller scale mechanisms within the system. (9-12)

• Proportional relationships (e.g. speed as the ratio of distance traveled to time taken) among different types of quantities provide information about the magnitude of properties and processes. (6-8)
• Phenomena that can be observed at one scale may not be observable at another scale. (6-8)

• Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)
  • Analyze data using computational models in order to make valid and reliable scientific claims. (9-12)

• Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)
  • Use a model to provide mechanistic accounts of phenomena. (9-12)

• Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)
  • Create a computational model or simulation of a phenomenon, designed device, process, or system. (9-12)

• Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)

• Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)

• Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

• 6-8: 4G/M5. A charged object can be charged in one of two ways, which we call either positively charged or negatively charged. Two objects that are charged in the same manner exert a force of repulsion on each other, while oppositely charged objects exert a force of attraction on each other.
• 9-12: 4G/H2a. Electric forces acting within and between atoms are vastly stronger than the gravitational forces acting between the atoms. At larger scales, gravitational forces accumulate to produce a large and noticeable effect, whereas electric forces tend to cancel each other out.

• 9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

• 6-8: 11D/M3. Natural phenomena often involve sizes, durations, and speeds that are extremely small or extremely large. These phenomena may be difficult to appreciate because they involve magnitudes far outside human experience.

Now in HTML5 Learners move charges around a simulated electric field to determine how certain variables affect interactions among charged bodies. Drag positive and negative charges onto the field and watch the resulting field lines. We like this model because it's easily adaptable for the middle school learner. It specifically meets NGSS content standard MS-PS2.B.ii about the relationship between field strength and distances between the interacting objects.

• Physical Sciences K-8 Electric Field Unit
• Physics First Electric Field Unit

Now in HTML5 This robust model lets students move charges around a simulated electric field to determine how certain variables affect interactions among charged bodies.  First, drag a positive or negative charge (or both) onto the field. The simulations allows you to place "E-Field Sensors", small positive test charges. Drag a sensor to display the voltage value at any point on the field or plot equipotential lines. A virtual tape measure is also provided to calculate distance.

• Conceptual Physics Electric Field Unit
• Algebra-Based Physics Electric Field Unit
• AP/Calculus-Based Physics Electric Field Unit