class2

Conceptual Checkpoint 19-3

  • A charge -q is positioned at either point A or point B, which are equidistant from two positive charges.

  • Inquiry:

    • Is the net force at point A (a) greater, (b) equal to, or (c) less than the net force at point B?

Electric Field and Coulomb's Law (Page 2)

  • Group of fixed charges exert a force F on a test charge (q<sub>test</sub>) at position r.

  • The electric field E at a point in space is defined as:

    • E = F/q<sub>test</sub>

  • It is the force per unit charge and is a vector function of position.

Electric Field of a Point Charge (Page 3)

  • Regarding a point charge Q, the electric field can be expressed as:

    • E = F/q<sub>test</sub>

    • This field is directed radially outward and diminishes with the square of distance, falling off as 1/r².

Analysis of Electric Fields (Page 4)

  • Electric Field Strength:

    • E<sub>net</sub> = E1 + E2 (Superposition principle)

  • Direction determined by charges:

    • Positive charge: Field lines point away.

    • Negative charge: Field lines point toward the charge.

Electric Field Lines (Page 5)

  • Definition: Electric field lines are continuous paths that indicate the direction of the electric field.

  • Properties:

    • Begin at positive charges or infinity, end at negative charges or infinity.

    • More dense where the electric field magnitude is greater.

Force Due to an Electric Field (Page 8)

  • The force F on a charge q in an electric field E at point r can be expressed as:

    • F = qE(r)

  • The direction of E indicates the direction a positive charge would move.

Electric Field Calculation (Page 9)

  • Given charges +2 mC at x = 1 m and x = -1 m:

    • Determine electric field at the origin (x = 0).

    • Plot the electric field along the +y axis.

    • Calculate the force on a +5 mC charge at an arbitrary location on the +y axis.

Electric Dipole (Pages 10 - 11)

  • An electric dipole consists of two charges, +q and -q, separated by distance d.

  • Dipole Moment (p):

    • Magnitude: p = qd

    • Direction: From -q to +q.

Behavior in Uniform Electric Field (Pages 12 - 17)

  • If placed in a uniform electric field:

    • Force: Total force on dipole = 0 due to equal and opposite forces on charges.

    • Rotation: While there's no linear acceleration, charges will rotate due to the torque acting on them (as forces are not colinear).

  • Torque (τ) is calculated as:

    • τ = F * d * sin(θ), where θ is the angle between p and E.

Electric Fields from Charge Distributions (Pages 20 - 36)

  • The net electric field of a charge distribution can be evaluated via the superposition principle:

    • Summation of electric fields from individual charges or differential charge elements.

  • Continuous charge distributions are analyzed by breaking them into infinitesimal pieces:

    • Electric Field Calculation: Each small piece of charge dq contributes to the electric field, forming an integral when summed over the charge distribution.

  • For different geometries (lines, rings, sheets), the charge density is defined as follows:

    • Linear density (λ): Q/L

    • Surface density (σ): Q/A

    • Volume density (ρ): Q/V

  • Differential charges are given by:

    • dq = λdL (line), dq = σdA (area), dq = ρdV (volume).

  • Example of a ring of charge:

    • Analyze symmetry to resolve the electric field at a point along the axis by integrating contributions from each differential charge.