Electrostatics

Static Electricity Static Electricity involves charges “at rest”. Fundamental Rule of Charge Opposite charges attract Like charges repel 3 methods of charging : friction, conduction, & induction

Electric Charges Electrons have a negative charge Protons have a positive charge Unit of Charge: Coulomb (C) Symbol for charge: q Elementary charge = 1.6 x 10-19 C One electron has a charge of -1.6 x 10-19 C One proton has a charge of +1.6 x 10-19 C

Methods of Charging Charging by friction – two neutral objects are rubbed together and become oppositely charged. The object that gains electrons becomes negatively charged and the one that loses electrons becomes positively charged. Charging by conduction – a charged object touches a neutral object so charges are transferred between objects until they reach charge equilibrium. The neutral object gets the same charge as the original charge. Charging by induction – a charged object is brought near but not touching a neutral object. The neutral object gets a charge separation or polariztion. The charge on the neutral object near the charged object is opposite that of the charging object. Unless grounded, it is a temporary charge.

Induction and Grounding If grounding is used along with induction, the neutral object will become permanently charged. It will have a charge opposite that of the charging object. This is done by grounding the neutral object on the side opposite the charging object. Grounding provides a path for the excess charge to flow to or from the ground.

Electroscopes Devices that detect that an object is charged Pith-ball electroscope - a foil covered styrofoam ball hanging by a thread Metal leaf electroscope - 2 metal leaves on the end of a metal rod enclosed in glass

Electroscopes – detecting charge The pith ball is attracted to the negative rod due to charge separation (induction) The metal leaves both get a negative charge (conduction) so they repel each other (spread apart) - - - - + - - - - - - - -

Conductors & Insulators - electrons flow easily - charge spreads over entire surface - examples: copper, gold, silver, aluminum, metals Insulators - electrons do not flow easily - charge stays where it was charged - examples: plastic, glass, rubber, wood, styrofoam

Electric Forces Coulomb’s Law: Use Coulomb’s Law to calculate the magnitude of the force between 2 charges. Unlike gravity, the forces can be either attractive or repulsive. Electric force is a vector and the force on q1 and the force on q2 are equal but opposite (Newton’s 3rd Law)! q1 q2 d + - Coulomb’s Law: F F + q1 q2 F FE = electrostatic force, Newtons (N) k = electric or Coulomb’s constant = 9 x 109 Nm2/C2 q1 = charge of the first object, C q2 = charge of the second object, C d = distance between the two charges (center to center), m

Direction of electric force If there are 2 like charges, the force will be repulsive. (Fe will be positive) If there are 2 unlike charges, the force will be repulsive. (Fe will be negative) Note: When finding net force for 3 or more charges, it is best to decide whether forces are attractive or repulsive and draw the force vectors rather than use the signs of Fe.

Electric Fields Electric fields are the “energy fields” that surround any charged particle or object Any charge placed in this field will experience a force. Electric fields are also vectors (magnitude & direction). The direction of an electric field is defined by the direction of the force on a tiny “+” test charge placed in that field. Thus electric fields are always in a direction that is away from “+” and toward “-”. Electric field lines are perpendicular to the surface of the charge and they never cross each other. They go away from a positive charge and toward a negative charge.

Electric Field Strength Electric Field strength or intensity is the force per unit charge and is measured in units of N/C (Newtons per Coulomb) E = Electric Field Strength or intensity, N/C Fe = Electrostatic Force, N qo = Charge placed in the electric field, C

Electric Field around a Charge Field around a Field around a Negative charge Positive charge - +

Electric field around two opposite charges

Electric Field around two like (positive) charges

Electric Field Strength at a point near a charge . q E + d E= electric field strength or intensity, N/C k = electric or Coulomb’s constant (= 9 x 109) q = charge causing the field, C d = distance from the charge to where the field strength is being measured, m

q = charge of the object causing the electric field, C Note - In the formulas on the previous slide and on the following slides q0 and q are described as follows: q = charge of the object causing the electric field, C qo = test charge or the charge of the object placed in the field, C

Vectors vs Scalars Electric Force and Electric Fields are vectors! All other quantities (Potential energy, work, electric potential difference, capacitance) are scalar quantities.

Electric Potential Difference Electric Potential Difference is the change in potential energy per unit charge at a given point due to an electric field. It is a scalar quantity. Units: Volts Potential Difference is required to make current flow. (1 Volt = 1 Joule / Coulomb) ΔV = Electric Potential Difference, Volts ΔPE =change in electric potential energy, J qo= charge placed in an electric field, C

Potential Difference at a Point ΔVP = Potential Difference at a point, V k = Coulomb’s constant = 9 x 109 Nm2/C2 q = Charge causing the electric potential, C d = distance between the charge q and where VP is being measured, m . d q VP

Potential Difference near several charges Although potential difference is a scalar quantity, it can be positive (if charge is positive) or negative (if charge is negative). To get the potential difference at a point near several charges, add up the potential differences due to each charge. Be sure to include the signs!

Equipotential and Field Lines Equipotential lines are lines of equal potential energy All points on each line have the same electric potential, V Equipotential lines are usually parallel to the surface of the charge and perpendicular to the electric field lines They do not depend on the sign of the charge Electric Field Lines ( E) Equipotential lines, each line has a different potential (V) For a point charge, they are concentric circles. +q

Electric Potential Energy between 2 charges The charges have the potential to move under the influence of the force between them. q1 q2 d

Electric Potential Energy and Electric Potential near charges PE and V are greatest farther from a negative charge. near a positive charge. - Low PE High PE + High PE Low PE

Work done on a charge So: W- the work required to move a charge through a potential difference, Joules (J) - magnitude of the charge moved through the field or potential difference, Coulombs (C) V - potential difference, Volts (V)

Note: No work is done in moving a charge along equipotential lines since there is no change in electric potential energy or electric potential.

Electric Potential of a charge being moved through a uniform electric field   Note: It must be a uniform electric field! Also there is no ∆PE and thus no ∆V if displacement is along equipotential lines (or perpendicular to the electric field).

Capacitor – a device used to store charge Capacitor – a device used to store charge. Example of a common simple capacitor: 2 oppositely charged plates To get more stored charge: increase the size of the plates decrease the plate separation increase the voltage of the battery - + E Note: This is an example of a uniform electric field. + - Insulator such as air – keeps charges separated battery

Capacitance – the ability of a conductor to store energy in the form of electrically separated charges C = Capacitance, Farads (F) Q = charge on one plate, C ∆V = Potential difference, V Note: 1 Farad = 1 Coulomb / Volt, same charge on each plate Also, a Farad is a very large unit so usually use μF or pF. (micro: μ = 10-6, nano: n = 10-9, pico: p = 10-12 )

Electrical Potential Energy Stored in a Capacitor  

Electrostatics Formulas     Note: The top two and next two equations look alike except for d2 vs d. The ones on the left are vector quantities and have d2 while the ones on the right have d and are not vectors.