Electrostatics/Electromagnetism

Net Electric Field Principle

Superposition Principle: Total electric field at a point is the vector sum of all individual electric fields at that point.

Direction of Electric Field Lines (Positive Charge)

Field lines radiate radially outward from the positive charge.

Direction of Electric Field Lines (Negative Charge)

Field lines radiate radially inward toward the negative charge.

Formula for Capacitance (Parallel)

Ceq=C1+C2+C3…Cn

Effect of Dielectrics on Capacitance

Inserting a dielectric always increases capacitance by a factor of K (the dielectric constant)

Relationship between Charge, Capacitance, and Voltage

Q=CV, where Q is charge. C is capacitance, and V is potential difference.

Work done by a Magnetic Field on a Moving Charge

Zero work. Since the magnetic force is always perpendicular to velocity, it cannot change the kinetic energy of the particle.

Equation for Magnetic Force on a Moving Charge

𝐹=|𝑞|𝑣𝐵sin𝜃 , where v is velocity, B is the magnetic field, and theta is the angle between them.

Equivalent Resistance (Series)

Req=R1+R2+….+Rn. The total resistance is always greater than any individual reistor.

Equivalent Resistance (Parallel)

1/Req=1/R1+1/R2+…+1/Rn. The total resistance is always smaller than the individual resistor.

Ohm’s Law

V=IR, where V is voltage, I is current, and R is resistance.

Gauss’ Law Formula

ΦE=(Qencl)/eo, where Φe is the electric flux and Qencl is the net charge enclosed by the surface.

Faraday Cage Operation

Electrostatic Shielding: Excess charge on a conductor resides on its outer surface, making the internal electric field zero.

Electric Field inside a Conductor

Zero (in electrostatic equilibrium). Charges redistribute themselves along the surface to cancel any internal field.

Charging by Induction

No contact required; results in the opposite charge sign.

Charging by Conduction

Requires contact, results in the same charge sign.

Electric Field Magnitude for a Dipole on the Bisector

The x-components cancel, and the y-components add together (or vice versa depending on orientation)

Current in Parallel Branches

Total current splits; branches with lower resistance carry higher current according to I=V/R

Voltage across a Charging Capacitor at t→ ∞

The voltage reaches its maximum, which is equal to the source voltage (Vo). Current becomes zero.

RC Time Constant (τ)

τ=RC. It represents the time required to charge a capacitor to ~63.2% of its final value.

Magnetic Field Path of a Perpendicular Charge

Circular Motion. The magnetic field acts as a centripetal force. (qvB=(mv²/r)

Coulomb’s Constant (k)

8.99e9 N*m²/C²

Net Flux through a surface with zero net charge

Zero flux. Flux only exists if there is a non-zero set charge enclosed by the surface.

Electric Force between Two Charges

FE=k |q1q2|/r² Follows an inverse-square relationship with distance

Tangent Law for Electrostatic Equilibrium

tan(theta)=qE/mg, used when a charged object hangs at an angle in an electric field.