MCAT Physics and Math - Electrostatics and Magnetism

Electrostatics

the study of stationary charges and the forces that are created by and which act upon these charges

proton

positively charged subatomic particle

electron

negatively charged subatomic particle

attractive forces

draw particles closer together, opposite signs

repulsive forces

push particles apart, same signs

ground

a means of returning charge to the earth

Static charge buildup/electricity

materials that are normally electrically neutral can acquire a net charge as result of friction; more significant in drier air because lower humidity makes it easier for charge to become and remain separated

coulomb (C)

SI unit of charge

fundamental unit of charge (e)

1.60 × 10⁻¹⁹ C

negative in electron, positive in proton

insulator

will not easly distribute a charge over its surface and will not transfer that charge to another neutral object very well; electrons tend to be closely linked with their respective nuclei

ex. most nonmetals

conductor

the charges will distribute approximately evenly upon the surface; able to transfer and transport charges and are oen used in circuits or electrochemical cells; nuclei surrounded by a sea of free electrons that are able to move rapidly throughout the material and are only loosely associated with the positive charges

ex. metals, ionic/electrolyte solutions

Coulomb’s law

quantifies the magnitude of the electrostatic force F_e between two charges

where Fe is the magnitude of the electrostatic force, k is Coulomb’s constant, q1 and q2 are the magnitudes of the two charges, and r is the distance between the charges

direction of the force may be obtained by remembering that unlike charges attract and like charges repel

Coulomb’s/electrostatic constant (k)

depends on units

permittivity of free space (ε₀)

a measure of how dense of an electric field is "permitted" to form in response to electric charges in a vacuum

8.8541878188(14)×10⁻¹² F⋅m⁻¹ (C²⋅kg⁻¹⋅m⁻³⋅s²)

Electric fields

Every electric charge sets up; make their presence known by exerting forces on other charges that move into the space of the field; vector quantity

where E is the electric field magnitude in newtons per coulomb, Fe is the magnitude of the force felt by the test charge q, k is the electrostatic constant, Q is the source charge magnitude, and r is the distance between the charges

test charge

the charge placed in the electric field

source charge

creates the electric field

Field lines

imaginary lines that represent how a positive test charge would move in the presence of the source charge; drawn in the direction of the actual electric field vectors and also indicate the relative strength of the electric field at a given point; Where the field lines are closer together, the field is stronger; where the lines are farther apart, the field is weaker

electric potential energy.

a form of potential energy that is dependent on the relative position of one charge with respect to another charge or to a collection of charges

electric potential

the ratio of the magnitude of a charge’s electric potential energy to the magnitude of the charge itself

volts (V)

unit of electric potential, = J/C

Coulomb’s Law derivatives

From left to right, multiply by r; from top to bottom, divide by q

potential difference/voltage

exist between two points that are at different distances from the source charge

where W_ab is the work needed to move a test charge q through an electric field from point a to point b.

equipotential line

a line on which the potential at every point is the same; the potential difference between any two points is zero

electric dipole

results from two equal and opposite charges being separated a small distance d from each other; transient or permanent

electric potential of dipoles

the scalar sum of the potentials due to each charge at that point

r1 - r2 ≈ d cos θ

dipole moment (p)

product of charge and separation distance; SI units of C · m; vector from the negative charge toward the positive charge (chem: pos (w/ crosshatch) to neg)

p = qd

perpendicular bisector of the dipole

the plane that lies halfway between +q and –q; the electrical potential at any point along this plane is 0

electric field vectors at the points along the perpendicular bisector will point in the direction opposite to p

net torque about the center of the dipole axis

τ = pE sin θ

where p is the magnitude of the dipole moment (p = qd), E is the magnitude of the uniform external electric field, and θ is the angle the dipole moment makes with the electric field.

magnetic field

created by moving charge; may be set up by the movement of individual charges, by the mass movement of charge in the form of a current though a conductive material, or by permanent magnets

tesla (T)

the SI unit for magnetic field strength; N*s/m*C

gauss

1 T = 10⁴ gauss

Diamagnetic materials

made of atoms with no unpaired electrons and that have no net magnetic field; slightly repelled by a magnet and so can be called weakly antimagnetic

ex. wood, plastics, water, glass, and skin

Paramagnetic materials

unpaired electrons; weakly magnetized in the presence of an external magnetic field, aligning the magnetic dipoles of the material with the external field; Upon removal of the external field, individual magnetic dipoles to reorient randomly.

ex. aluminum, copper, and gold

Ferromagnetic materials

unpaired electrons and permanent atomic magnetic dipoles that are normally oriented randomly; become strongly magnetized when exposed to a magnetic field or under certain temperatures; Field lines exit the north pole and enter the south pole

ex. iron, nickel, and cobalt

infinitely long and straight current-carrying wire magnet

permeability of free space (μ₀)

1.25663706127(20)×10⁻⁶ kg⋅m⋅s⁻²⋅A⁻²

right-hand rule

1. Point your thumb in the direction of the current and wrap your fingers around the current-carrying wire. Your fingers then mimic the circular field lines, curling around the wire.

2. To determine the direction of the magnetic force on a moving charge, first position your right thumb in the direction of the velocity vector. Then, put your fingers in the direction of the magnetic field lines. Your palm will point in the direction of the force vector for a positive charge, whereas the back of your hand will point in the direction of the force vector for a negative charge.

circular loop of current-carrying wire magnet

Lorentz force

the sum of electrostatic and magnetic forces

magnetic force

where q is the charge, v is the magnitude of its velocity, B is the magnitude of the magnetic field, and θ is the smallest angle between the velocity vector v and the magnetic field vector B; perpendicular component

Force on a Current-Carrying Wire

where I is the current, L is the length of the wire in the field, B is the magnitude of the magnetic field, and θ is the angle between L and B.