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

Superposition: Adding Coulomb Forces as Vectors

How do you add the Coulomb forces from several charges as vectors, component by component?

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Your summary note

1. The superposition principle $\vec{F}_j = \sum_{i \neq j} \vec{F}_{ij}$
  State the rule for three charges and for $N$ charges, and record that each pair force is independent of the other charges when all charges are held at fixed positions.
2. Three charges on a square, added by components
  Work the example with $q_2 = -q_1$ : write $\hat{r}_{13}$ and $\hat{r}_{23}$ in $\hat{i}$ , $\hat{j}$ components, use $r_{13} = \sqrt{2}\,a$ , keep the sign of $q_2$ , and reach $F_3 = 3.0 \times 10^2$ N.
3. Choosing the arctangent solution by quadrant
  Compute $\phi = \tan^{-1}(F_{3,y}/F_{3,x})$ , list both solutions $151.3^\circ$ and $-28.7^\circ$ , and record how the signs of the force components select $151.3^\circ$ .
Attempt 1 of 2