Electromagnetism Physics - Electric Charges and Fields

Explain Coulomb’s law in vector form for two charges, deriving the force as k q1 q2 / r^2 along the separation vector and noting F12 and F21 opposite.

Use Coulomb’s law in vector form to compute the force between two point charges, building the position vector, its magnitude, and the unit vector, then apply the three meters separation.

Explore potential energy of a single charge in an external electric field, where work equals q times the electric potential, and prepare for more cases.

Explore electric flux as the number of lines of force through a surface, defined by the dot product of the electric field and the area vector, indicating outgoing flux.

Explore Gauss's law and its use to relate the total charge enclosed by a surface to the electric flux, through applications to spherical shells, cylinders, and plane surfaces.

Derives the electric field of a quarter-circle arc of charge by integrating dl with lambda and summing x and y components, yielding e = sqrt(2) k lambda / r.

derive a general expression for the electric field from a charged arc by resolving dE into components, using symmetry, and integrating to obtain E = 2kλ / sin(alpha/2).

Explore the electric field and electric field intensity around charges, including how a test charge experiences force from a source charge and the field's vector direction and units in N/C.

Compute the electric field from a point charge using the position vector, its magnitude, and unit vector; express E in vector form as E = k q r / r^3.

Compute electric field intensity in vector form for a 20 microcoulomb charge at the origin and the point (2, 1, 2) using the position vector.

Explore the motion of a charged particle, like an electron, in a uniform electric field between two plates. Show how the y deflection scales with the charge-to-mass ratio.

Electric lines of forces show the electric field: they emanate from positive charges and enter negative charges, never intersect, and tangents indicate field direction.

Derive the electric field on the axis of a charged ring by resolving components and setting up an integral, linking ring radius and axial distance to the field.

Explore the electric field due to a point charge, using e = k q / r^2 to show how charge and distance shape the field.

Introduces linear charge density, lambda equals q over l, and its use for charge distribution along a line, plus the arc length formula, arc equals radius times central angle.

Compute the electric field from a semicircular line charge by integrating along the arc, resolving into components, and obtain E = 2 k lambda / r.

Derive the electric field intensity for a point charge at distance r using Coulomb's law, showing E is proportional to Q and inversely proportional to r^2.

Redistribute charges when two separated charges touch, conserving total charge and equalizing to Q'=(Q1+Q2)/2, while the ratio F_after to F_before equals (Q1+Q2)^2/(4Q1Q2).

Compute the redistribution of charges after contact and evaluate the ratio of the resulting post-contact force to the pre-contact force, using charges and inverse-square distance.

Explore how inserting a dielectric polarizes in an electric field, producing an opposing field that reduces the net electric field; this polarization lays the groundwork for capacitors.

This lecture presents dielectrics as insulating materials that store electric charge, defines dielectric constant (relative permittivity), and contrasts polar versus non-polar dielectrics by dipole moments.

Align molecular dipoles in polar dielectrics with an electric field to produce a net dipole moment and polarization, related to electric susceptibility and its zero value in vacuum.

Understand how non-polar dielectrics polarize when placed in an electric field, creating induced dipoles and dipole moments, and compare with polar molecules.

Explore torque on a dipole in electric field; derive p = qd and torque = p E sin θ, showing when torque is maximum at 90° and minimum at 0°/180°.

Apply Gauss's law to a uniformly charged plane sheet to derive the electric field and relate it to the surface charge density sigma, and reinforce practice for exams.

Apply Gauss's law to a uniformly charged sphere using a Gaussian surface to derive the electric field and flux, showing the outside field is Q/(4 pi epsilon0 r^2).

Apply Gauss's law to a uniformly charged cylinder with a coaxial Gaussian surface to derive the electric field in terms of the linear charge density lambda (Q/L).

Derive the electric field of a charged rod by integrating differential elements from a to a+L, using lambda = Q/L, yielding E = k lambda L / (a(a+L)).

Compute the electric field from a long charged rod at distance a by integrating along the rod with linear charge density lambda, yielding E = (lambda/8)(sin theta2 + sin theta1).

Analyze the axis electric field of a charged ring and identify the maximum field and its position: x = r/√2 and Emax = 2kq/(3√3 r^2), and sketch E versus x.

Identify neutral points where electric fields from two charges cancel on the line between them for like and unlike charges; equate fields to locate the equilibrium and plot total-field graph.

This lecture analyzes the neutral point between two charges, including unlike charges, lying on the line joining them closer to the smaller magnitude charge where the electric field is zero.

Explore stable and unstable equilibrium for a test charge between two like charges, showing how displacement restores or diverges, and noting how charge signs determine the type of equilibrium.

Explore how two like charges achieve equilibrium along the line joining them by balancing Coulomb forces with a test charge, deriving x = r√Q1/(√Q1+√Q2).

Learn how two unlike charges reach equilibrium by placing a third charge nearer the smaller magnitude charge, and derive the distance x from the charges’ square roots.

Determine the third charge Q0 needed to achieve stable equilibrium for two charges Q1 and Q2 at a given separation, using distances r1 and r2 and the square-root relations.

three equal charges at the triangle's vertices create two equal forces that sum to a sqrt(3) F at 60 degrees; the central charge must balance this, giving Q0 = -Q/3.

analyze a triangle with three charges of one microcoulomb at its vertices and use a shortcut formula to determine the central charge.