Electric forces and electric fields

1. Proprieties of electric charges Electric charge can be + or – Like charges repel one another; and unlike charges attract one another Electric charge is always conserved

The object become charged because – charge is transferred from one object to another An object may have charge of ±e, ±2e, ±3e e = 1.60219x10-19C SI unit: C (Coulomb) 2 Insulators and conductors In conductors, electric charges move freely in response to an electric force. All other materials are called insulators (give an ex. of each) Semiconductors are between conductors and insulators.

An object connected to a conducting wire buried in the Earth is said to be grounded. Induction – charging of a conductor Charging an object by induction requires no contact with the object inducing the charge.

3. Coulomb’s Law An electric force has the following properties: It is directing along a line joining the two particles and is inversely proportional to the square of the separation distance r, between them It is proportional to the product of the magnitudes of the charges, |q1|and |q2|, of the 2 particles It is attractive if the charges are of the opposite sign, and repulsive if the charges have the same sign

The magnitude of the electric force: F=ke (|q1||q2|/r2) ke – Coulomb constant ke = 8.9875x109N m2/C2

4. Electric Field The electric field E produced by a charge Q at the location of a small “test” charge qo is defined as the electric force F exerted by Q and qo divided by the charge qo . E=F/qo E=ke (|q|/r2) Si unit : N/C

Pb. Strategies: 1. Draw a diagram of the charges 2. Identify the charge of interest 3. Convert all units in SI 4. Apply Coulomb’s Law 5. Sum all the x- components of the resulting electric force 6. Sum all the y-components of the resulting electric force 7. Use Pythagorean theorem to find the magnitude and the direction of the force

5. Electric field lines 1. The electric field E is tangent to the electric field lines at each point 2. The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region

Rules for drawing electric field lines: -The lines for a group of point charges must begin on + charge and end on – charge - The number of lines drawn leaving a + charge or ending a – charge is proportional to the magnitude of the charge - No two field lines can cross each other

6. Conductors in electrostatic equilibrium When no net motion of charge occurs within a conductor, the conductor is in electrostatic equilibrium Proprieties of an isolated conductor: 1. the electric field is zero inside of the material 2. any excess charge on an isolated conductor resides entirely on its surface 3. the electric field just outside a charge conductor is perpendicular to the conductor’s surface 4. On an irregularly shaped conductor , the charge accumulates at sharp points, where the radius of curvature of the surface is smallest

7.electric flux and Gauss’s Law The electric flux ( the number of the field lines) is proportional to the product of the electric field and surface of the area ΦE =EA ΦE =EA cosθ

For a close surface, the flux line passing into the interior of the volume are negative, and those passing out of the interior of the volume are positive

Gauss’s Law: E= ke q|/r2 A= 4πr2 ΦE =EA=4π ke q ΦE =q/ εo Permittivity of free space: εo=1/(4π ke )=8.85x10-12C2/Nm2 The electric flux through any closed surface is equal to the net charge inside the surface divided by the permittivity

8. Potential difference and electrical potential Work and potential energy: Potential energy is a scalar quantity with change to the negative of the work done by the conservative force ΔPE=Pef-Pei =- Wf Coulomb force is conservative If imagine a small + charge placed in a uniform electric field E. As the charge moves from A to B, the work done on the charge by the electric field: W=FxΔx =q Ex (xf-xi)

Work –energy theorem W=q Ex Δx =ΔKE But the work done by a conservative force can be reinterpreted as the negative of the charge in a potential energy associated with that force ΔPE of a system consisting on an object of charge q through a displacement Δx in a constant electric field E is given by: ΔPE =-WAB= -q Ex Δx SI unit J (Joule)

Δ KE + ΔPE el = ΔKE +(0-ΙqΙ E d) =0 Similarly , KE equal in magnitude to the loss of gravitational potential energy: ΔKE +ΔPEg =ΔKE +(0 –mgd) =0 ΔKE=mgd

Electric Potential F = qE The electric potential difference between points A and B is the charge in electric potential energy as a charge q moves from A to B, divided by the charge q: ΔV =VA-VB = ΔPE/q SI unit J/C or V (Joule/Coulomb or Volt) Electric potential is a scalar quantity

Electric potential created by a point charge: V=ke q/r 9.Electric potential and potential energy due to point charges The electric field of a point charge extends throughout space, so its electrical potential also Electric potential created by a point charge: V=ke q/r The electric potential of two or more charges is obtained by applying the superposition principle: the total electric potential at some point P due to several point charges is the algebraic sum of the V due to the individual charges

The electric potential at all points on a charged conductor 10.Potentials and charged conductors The electric potential at all points on a charged conductor W= -ΔPE =-q( VB-VA) No net work is required to move a charge between two points that are at the same electric potential All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential

The electric potential is a constant everywhere on the surface of a charged conductor The electric potential is constant everywhere inside a conductor and equal to the same value at the surface The electron volt is defined as KE that an electron gains when accelerated through a potential difference of 1V 1eV =1.6x 10-19 C V =1.6x10-19 J

Equipotential surface is a surface on which all points are at the same potential The electric field at every point of an equipotential surface is perpendicular to the surface.

11.Capacitance A capacitor- is a device used in variety of electric circuits The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between conductors (plates) C=Q/ΔV SI unit F (Farad)=C/V

12.The parallel-plate capacitor C=q/ΔV ΔV=Ed; E=σ/ε0 ; q=σA C=σA/Ed=σA/(σε0)d C= ε0A/d

Symbols for circuit elements and circuits

13 Combinations of capacitors Capacitor in Parallel

Capacitors in parallel both have the same potential difference across them Q=Q1+Q2 Q1= C1ΔV Q2 = C2ΔV Q= Ceq ΔV CeqΔV=C1ΔV+C2ΔV Ceq=C1+C2 (parallel combination)

Capacitors in series

Electrical Energy and Capacitance For a series combination of capacitors, the magnitude of the charge must be the same on all the plates ΔV=Q/Ceq ΔV1=Q/C1; ΔV2=Q/C2; ΔV=ΔV1+ΔV2 Q/C= Q/C1+Q/C2 1/C= 1/C1+1/C2 (series combination) Electrical Energy and Capacitance

14. Capacitors with dielectrics

A Dielectric- is an insulating material (rubber, plastic, waxed paper) If a dielectric is inserted between the plates, the voltage across the plates is reduced by a factor k (dielectric constant) to the value: ΔV =ΔV0/k C=k C0 C=kε0 A/d The maximum electric field is called dielectric strength