EC-2.1 Vector Calculus and the Static Electric Field
You can work with gradient, divergence and curl in the coordinate system a problem suggests, apply the divergence and Stokes theorems, and find fields, potentials and capacitance for the standard symmetric arrangements.
Electromagnetics is written in vector calculus, and most of the difficulty students report with the subject is really difficulty with the notation rather than with the physics. So this topic builds the notation first and then spends it on the static electric field, where the results are already familiar from earlier physics and can be checked against intuition. The two integral theorems here are the ones that convert Maxwell's equations between their differential and integral forms later, so they are worth more than the time they take.
Work through these
Coordinate systems, and choosing the one the symmetry hands you
Cartesian, cylindrical and spherical coordinates describe the same space, and a problem with a symmetry becomes far shorter in the system that matches it. Converting a vector between systems is mechanical and worth practising until it is automatic.
NPTEL: Electromagnetic Fields · CourseGradient, divergence and curl: what each one measures
The gradient points the way a scalar increases fastest, the divergence measures what a field is flowing out of a point, and the curl measures its circulation around one. Attaching that meaning to each symbol makes the equations later read as sentences.
MIT OpenCourseWare 8.02: Physics II — Electricity and Magnetism · CourseThe divergence theorem and Stokes' theorem, and what they let you exchange
One converts a volume integral of divergence into a surface integral, the other a surface integral of curl into a line integral around its edge. These two conversions are what turn Maxwell's equations from one form into the other.
Coulomb's law and Gauss's law, and when the symmetry makes the second one easy
Adding contributions works always and is laborious; enclosing the charge in a surface the field crosses uniformly works only with symmetry but takes a line. Recognising which situation you are in is the whole judgement here.
NPTEL: Electromagnetic Fields · CoursePotential, and why the field is its gradient with a sign
The electric field is conservative in the static case, so a single scalar carries all the information and is easier to compute with. The minus sign says the field points from high potential to low, which is worth saying aloud rather than memorising.
Dielectrics, capacitance, and the boundary conditions at an interface
A dielectric polarises and reduces the field inside it, which is what capacitance measures. At an interface the tangential field and the normal flux density are the quantities that carry across, and those two rules solve most interface problems.
NPTEL: Electromagnetic Theory · Course
Sign in to keep your progress.
Free resources
We haven't checked most of these for screen reader use yet.
Links last checked 3 Sept 2026.
Stuck here?
Ask a mentor. A real person answers, and they can see exactly which topic you're on. Usually within a couple of working days.
Checking your session…
Topics shown in module order.