All charged objects produce a thing we call their electric field. It is not observable in the conventional sense and might be thought of as a clever way to keep track of how charged objects interact. The field from one electron can influence another electron and the result is they feel a repelling force. 

Large electric fields are in the atmosphere during storms.

Big Ideas

Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.

Bid Idea 2: Fields existing in space can be used to explain interactions.

Big Idea 3: The interactions of an object with other objects can be described by forces.

Big Idea 4: Interactions between systems can result in changes in those systems.

Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.

 

Learning Objectives

BoxSand Learning Objectives

Electric-Fields-Potentials.Electric-Fields.LO.BS.1: Be able to interpret electric field diagrams

Electric-Fields-Potentials.Electric-Fields.LO.BS.2: Be able to calculate the electric field for a point charge or a group of point charges

Electric-Fields-Potentials.Electric-Fields.LO.BS.3: Be able to explain the $\Delta \hat{r}$ unit vector and apply it mathamatically to problems

Electric-Fields-Potentials.Electric-Fields.LO.BS.4: Be able to find the force of a charged particle in an electric field

Electric-Fields-Potentials.Electric-Fields.LO.BS.5: Be able to roughly sketch or identify the field for simple charge distributions

Electric-Fields-Potentials.Electric-Fields.LO.BS.6: Be able to explain the concept of a field and how it pertains to the electric field

Electric-Fields-Potentials.Electric-Fields.LO.BS.7: Students should understand the concept of electric field, so they can:

  1.  Define it in terms of the force on a test charge.
  2. Describe and calculate the electric field of a single point charge.
  3. Calculate the magnitude and direction of the electric field produced by two or more point charges.
  4. Calculate the magnitude and direction of the force on a positive or negative charge placed in a specified field.
  5. Interpret an electric field diagram
  6. Analyze the motion of a particle of specified charge and mass in a uniform electric field.

Electric-Fields-Potentials.Electric-Fields.LO.BS.8: Students should understand the nature of electric fields in and around conductors, so they can:

  1. Explain the mechanics responsible for the absence of electric field inside a conductor, and know that all excess charge must reside on the surface of the conductor.
  2. Explain why a conductor must be an equipotential, and apply this principle in analyzing what happens when conductors are connected by wires.
  3. Show that all excess charge on a conductor must reside on its surface and that the field outside the conductor must be perpendicular to the surface
  4. Describe and sketch a graph of the electric field and potential inside and outside a charged conducting sphere.

College Board Learning Objectives

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.1.1: The student is able to predict the direction and the magnitude of the force exerted on an object with an electric charge q placed in an electric field E using the mathematical model of the relation between an electric force and an electric field: $\vec{F}=q\vec{E} $; a vector relation. [SP 6.4, 7.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.1.2: The student is able to calculate any one of the variables — electric force, electric charge, and electric field — at a point given the values and sign or direction of the other two quantities. [SP 2.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.2.1: The student is able to qualitatively and semiquantitatively apply the vector relationship between the electric field and the net electric charge creating that field. [SP 2.2, 6.4]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.3.1: The student is able to explain the inverse square dependence of the electric field surrounding a spherically symmetric electrically charged object. [SP 6.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.4.1: The student is able to distinguish the characteristics that differ between monopole fields (gravitational field of spherical mass and electrical field due to single point charge) and dipole fields (electric dipole field and magnetic field) and make claims about the spatial behavior of the fields using qualitative or semiquantitative arguments based on vector addition of fields due to each point source, including identifying the locations and signs of sources from a vector diagram of the field. [SP 2.2, 6.4, 7.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.4.2: The student is able to apply mathematical routines to determine the magnitude and direction of the electric field at specified points in the vicinity of a small set (2–4) of point charges and express the results in terms of magnitude and direction of the field in a visual representation by drawing field vectors of appropriate length and direction at the specified points. [SP 1.4, 2.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.5.1: The student is able to create representations of the magnitude and direction of the electric field at various distances (small compared to plate size) from two electrically charged plates of equal magnitude and opposite signs, and is able to recognize that the assumption of uniform field is not appropriate near edges of plates. [SP 1.1, 2.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.5.2: The student is able to calculate the magnitude and determine the direction of the electric field between two electrically charged parallel plates, given the charge of each plate, or the electric potential difference and plate separation. [SP 2.2]

Electric-Fields-Potentials.Electric-Fields.LO.CB.2.C.5.3: The student is able to represent the motion of an electrically charged particle in the uniform field between two oppositely charged plates and express the connection of this motion to projectile motion of an object with mass in the Earth’s gravitational field. [SP 1.1, 2.2, 7.1]

Enduring Understanding and Essential Knowledge

Enduring Understanding

Essential Knowledge

Electric-Fields-Potentials.Electric-Fields.EU.CB.2.A: A field associates a value of some physical quantity with every point in space. Field models are useful for describing interactions that occur at a distance (long-range forces) as well as a variety of other physical phenomena.

  Electric-Fields-Potentials.Electric-Fields.EK.CB.2.A.1: A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector.

  1. Vector fields are represented by field vectors indicating direction and magnitude.
  2. When more than one source object with mass or electric charge is present, the field value can be determined by vector addition.
  3. Conversely, a known vector field can be used to make inferences about the number, relative size, and location of sources.

 

Electric-Fields-Potentials.Electric-Fields.EK.CB.2.A.2: A scalar field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a scalar. In Physics 2, this should include electric potential.

  1. Scalar fields are represented by field values.
  2. When more than one source object with mass or charge is present, the scalar field value can be determined by scalar addition.
  3. Conversely, a known scalar field can be used to make inferences about the number, relative size, and location of sources.
Electric-Fields-Potentials.Electric-Fields.EU.CB.2.C: An electric field is caused by an object with electric charge.

Electric-Fields-Potentials.Electric-Fields.EK.CB.2.C.1: The magnitude of the electric force Fexerted on an object with electric charge q by an electric field E is $\vec{F}=q\vec{E}$. The direction of the force is determined by the direction of the field and the sign of the charge, with positively charged objects accelerating in the direction of the field and negatively charged objects accelerating in the direction opposite the field. This should include a vector field map for positive point charges, negative point charges, spherically symmetric charge distributions, and uniformly charged parallel plates.

Electric-Fields-Potentials.Electric-Fields.EK.CB2.C.2: The magnitude of the electric field vector is proportional to the net electric charge of the object(s) creating that field. This includes positive point charges, negative point charges, spherically symmetric charge distributions, and uniformly charged parallel plates. 

Electric-Fields-Potentials.Electric-Fields.EK.CB.2.C.3: The electric field outside a spherically symmetric charged object is radial and its magnitude varies as the inverse square of the radial distance from the center of that object. Electric field lines are not in the curriculum. Students will be expected to rely only on the rough intuitive sense underlying field lines, wherein the field is viewed as analogous to something emanating uniformly from a source.

  1. The inverse square relation known as Coulomb’s law gives the magnitude of the electric field at a distance r from the center of a source object of electric charge Q as

    $E=\frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^{2}}$
  2. This relation is based on a model of the space surrounding a charged source object by considering the radial dependence of the area of the surface of a sphere centered on the source object.

Electric-Fields-Potentials.Electric-Fields.EK.CB2.C.4: The electric field around dipoles and other systems of electrically charged objects (that can be modeled as point objects) is found by vector addition of the field of each individual object. Electric dipoles are treated qualitatively in this course as a teaching analogy to facilitate student understanding of magnetic dipoles.

  1. When an object is small compared to the distances involved in the problem, or when a larger object is being modeled as a large number of very small constituent particles, these can be modeled as charged objects of negligible size, or “point charges.”
  2. The expression for the electric field due to a point charge can be used to determine the electric field, either qualitatively or quantitatively, around a simple, highly symmetric distribution of point charges.

Relevant Equation:

$E = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^{2}}$

Electric-Fields-Potentials.Electric-Fields.EK.CB2.C.5: Between two oppositely charged parallel plates with uniformly distributed electric charge, at points far from the edges of the plates, the electric field is perpendicular to the plates and is constant in both magnitude and direction.

Relevant Equations:

$E=\frac{Q}{\epsilon_{0} A}$

$E =\frac{\Delta V}{\Delta r}$

$\Delta V = \frac{Q}{C}$

$U_{c} = \frac{1}{2}Q \Delta V = \frac{1}{2}C(\Delta V)^{2}$

 
   
   

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