Electricity and Magnetism

Mathematical Tools and Fields

01Series Approximations: Keeping One or Two Terms 02Integrals as Sums: Along a Line and a Curved Path 03Line Integrals: Work as the Integral of F · ds 04Closed Line Integrals: Work Around a Loop 05Double Integrals: Area, Charge and Volume 06Closed Surface Integrals: The Sphere and Its Charge 07Electric Flux Through Surfaces and Volume Integrals Problem set0/10 Problem set 20/10 MIT problem set0/4

01Field Theory Versus Action at a Distance 02Scalar Fields: Contour, Color and Relief Maps 03Vector Fields, Sources, Sinks and Divergence 04Curl: Measuring the Circulation of a Field 05Gravitational, Electric and Magnetic Fields 06Drawing Vector Fields: Arrows, Lines and Grass Seeds Problem set0/10 Problem set 20/10 MIT problem set0/1

Electrostatics

01Coulomb's Law: Force Between Two Point Charges 02Superposition: Adding Coulomb Forces as Vectors 03Field Lines, Null Points and Uniform Fields 04The Electric Dipole and Its 1/r³ Field 05Torque, Energy and Force on a Dipole in a Field Problem set0/10 Problem set 20/10 MIT problem set0/1

Field Lines, Null Points and Uniform Fields

Where does the field of two charges vanish, and what do field lines reveal about charges and uniform fields?

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Your summary note

1. The electric field $\vec{E} = \lim_{q_0 \to 0} \vec{F}_e/q_0$
  Write the test-charge definition beside its gravitational analogue $\vec{g}$ , combine it with Coulomb's law to get the point-charge field, add the sum $\vec{E} = \sum_i \vec{E}_i$ , and record $\vec{F}_e = q_0\vec{E}$ .
2. Field-line pattern of a charge pair from four considerations
  Sketch the field lines of a charge pair and annotate how symmetry, the near field, the far field of $Q = \sum_i Q_i$ , and null points where $\vec{E} = \vec{0}$ each shape the picture.
3. The four properties of field lines
  List them: $\vec{E}$ tangent to the line, lines starting on positive and ending on negative charges or at infinity, line count proportional to charge, and no two lines crossing.
4. Charge released from rest between parallel plates
  Derive $\vec{a} = q\vec{E}/m$ , $v = \sqrt{2yqE_y/m}$ and $K = qE_y y$ with units checked, and record that the kinetic energy comes from the field while the momentum comes from the source charges.
Attempt 1 of 2