physics module 20

newton’s first law: a body in uniform motion remains in uniform motion and a body at rest remains at rest, unless acted on by a nonzero net force.

newton’s second law: the rate at which a body’s momentum changes is equal to the net force acting on the body: F = dp/dt = mdv/dt = ma

g (gravitational field at a point of mass m) = -G M (gravitating mass/r² (the distance from the center of M to the point where the field is being evaluated) * unit vector pointing radially away from M

electron charge = -proton charge

the magnitude of this charge is the elementary charge e. electric charge only comes in discrete amounts (quantized).

CHARGE is represented by the coulomb (C).

e = 1.602 × 10^-19 C.

A coulomb is 6.24 × 10^18 elementary charges.

Coulomb's Law:

Where:

• f is the force between the charges

• k is the electrostatic constant (also known as Coulomb's constant) (9×10^9 N*m²/C²)

• q1 and q2 are the magnitudes of the charges

• r is the distance between the charges

• r hat determines the direction

1. Identify the charge or charges you want to calculate the force.

2. identify the charge producing the force.

3. comprise the source charge.

Coulomb’s law is strictly only true for point charges (negligible size). Electrons and protons are treated as protons, and, if the distance is big enough, any two objects can be point charges.

Charge distributions are arrangements of charge spread over space.

Superposition principle is the fact that electric forces add vectorially.

Gravitational field is a set of vectors giving the magnitude and direction of the gravitational force per unit mass at each point. We can do the same thing for electric force (force per unit charge).

F (electric force) = q (small test charge) * E (electric field at any point)

Test charge is the charge we’re using to probe the field. If it’s large, the field it creates may disturb the source charges. It’s important to use small test charges.

If q is positive, then the force is in the same direction as the field. If it is negative, the force is opposite to the field direction.

E is N(ewtons)/C(oulomb).

Electric field exists with or without a charge, but electric force only arises when a charge is present.

microcoulombs is 10^-6 of a regular coulomb.

F is N(ewtons).

E = (F OR kqq/r² r hat) / q = kq/r² r hat (always points away from q)

Electric force obeys the superposition, and so does electric field.

E = E1 + E2 + E3…

nanometer is 10^-9 meter.

meganewton is 10^6 newton.

nanonewton is 10^-9 newton.

giganewton is 10^9 newton.

far away, the distance between two charges becomes negligible, so the stronger charge will dominate.

electric dipole consists of two point charges of equal magnitude but opposite sign.

a is only negligible if it is compared to y. if it is not negligible, we can’t neglect it.

electric dipole moment p = q (charge) d (separation)

volume charge density ρ with units of C/m³

surface charge density σ with units C/m²

line charge density λ with units C/m

E (continuous distribution of charges) = ∫dE (determined by integrating the fields of infinitesimal charge elements) = ∫(kdq (infinitesimal charge element) /r² (the distance from dq to the point of evaluation))r̂ (unit vector that points away from dq) = kQx/(x²+a²)^(3/2)

F = qE

F = ma

so,

ma = qE

a = qE/m

When a field us uniform, there is a constant acceleration of the proton or electron.

v²/r applies to circular motion = a.

a = v²/r

When a dipole experiences two opposing forces, it experiences a torque. torque = radius * force. (force sin theta).

change in potential energy is equal to negative work.

E = 2kλ/r