Télécharger la présentation
## Lecture 04

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Lecture 04**The Electric Field Chapter 22 - HRW Electric Field**Physics 2049 News**• WebAssign was due today • Another one is posted for Friday • You should be reading chapter 22; The Electric Field. • This is a very important concept. • It is a little “mathy” • There will be a QUIZ on Friday. • Material from chapters 21-22. • Studying Works! Electric Field**This is WAR**Ming the merciless this guy is MEAN! • You are fighting the enemy on the planet Mongo. • The evil emperor Ming’s forces are behind a strange green haze. • You aim your blaster and fire … but …… Electric Field**Nothing Happens! The Green thing is a Force Field!**The Force may not be with you …. Electric Field**Side View**The FORCE FIELD Force Big! |Force| o Position Electric Field**Properties of a FORCE FIELD**• It is a property of the position in space. • There is a cause but that cause may not be known. • The force on an object is usually proportional to some property of an object which is placed into the field. Electric Field**EXAMPLE: The Gravitational Field That We Live In.**M m mg Mg Electric Field**The gravitational field: g**• The gravitational field strength is defined as the Force per unit mass that the field creates on an object • This becomes g=(F/m)=(mg/m)=g • The field strength is a VECTOR. • For this case, the gravitational field is constant. • magnitude=g (9.8 m/s) • direction= down Electric Field**Final Comment on Gravitational Field:**Even though we know what is causing the force, we really don’t usually think about it. Electric Field**Newton’s Law of Gravitation**m R Electric Field MEarth**The Calculation**Electric Field**Not quite correct ….**Earth and the Moon (in background), seen from space) Electric Field**More better …**Moon Fmoon m mg FEarth Electric Field MEarth**To be more precise …**• g is caused by • Earth (MAJOR) • moon (small) • Sun (smaller yet) • Mongo (extremely teeny tiny) • g is therefore a function of position on the Earth and even on the time of the year or day. Electric Field**The Electric Field E**• In a SIMILAR WAY • We DEFINE the ELECTRIC FIELD STRENGTH AS BEING THE FORCE PER UNIT CHARGE. • Place a charge q at a point in space. • Measure (or sense) the force on the charge – F • Calculate the Electric Field by dividing the Force by the charge, Electric Field**Electric Field Near a Charge**Electric Field**Two (+) Charges**Electric Field**Two Opposite Charges**Electric Field**A First Calculation**Q A Charge r q The spot where we want to know the Electric Field Place a “test charge at the point and measure the Force on it. Electric Field**Doing it**Q A Charge r F q The spot where we want to know the Electric Field Electric Field**General-**Electric Field**Continuous Charge Distribution**Electric Field**ymmetry**Electric Field**Let’s Do it Real Time**Concept – Charge per unit length m dq= mds Electric Field**The math**Why? Electric Field**q**dEy dE q r x dx L setup A Harder Problem A line of charge m=charge/length Electric Field**(standard integral)**Electric Field**Completing the Math**1/r dependence Electric Field**Dare we project this??**• Point Charge goes as 1/r2 • Infinite line of charge goes as 1/r1 • Could it be possible that the field of an infinite plane of charge could go as 1/r0? A constant?? Let's look at it... Electric Field**The Geometry**Define surface charge density s=charge/unit-area dq=sdA (z2+r2)1/2 dA=2prdr dq=s x dA = 2psrdr Electric Field**(z2+r2)1/2**q Electric Field**(z2+r2)1/2**Final Result Electric Field**Look at the “Field Lines”**Electric Field**What did we learn in this chapter??**• We introduced the concept of the Electric FIELD. • We may not know what causes the field. (The evil Emperor Ming) • If we know where all the charges are we can CALCULATE E. • E is a VECTOR. • The equation for E is the same as for the force on a charge from Coulomb’s Law but divided by the “q of the test charge”. Electric Field**What else did we learn in this chapter?**• We introduced continuous distributions of charge rather than individual discrete charges. • Instead of adding the individual charges we must INTEGRATE the (dq)s. • There are three kinds of continuously distributed charges. Electric Field**Kinds of continuously distributed charges**• Line of charge • m or sometimes l = the charge per unit length. • dq=mds (ds= differential of length along the line) • Area • s = charge per unit area • dq=sdA • dA = dxdy (rectangular coordinates) • dA= 2prdr for elemental ring of charge • Volume • r=charge per unit volume • dq=rdV • dV=dxdydz or 4pr2dr or some other expressions we will look at later. Electric Field**The Sphere**dq r thk=dr dq=rdV=r x surface area x thickness =r x 4pr2 x dr Electric Field**Summary**(Note: I left off the unit vectors in the last equation set, but be aware that they should be there.) Electric Field**To be remembered …**• If the ELECTRIC FIELD at a point is E, then • E=F/q (This is the definition!) • Using some advancedmathematics we can derive from this equation, the fact that: REMEMBER THIS ! Electric Field**Example:**Electric Field**Solution**Electric Field**q1 = -9q**q2=+2q In the Figure, particle 1 of charge q1 = -9.00q and particle 2 of charge q2 = +2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero?[1.89]L(b) Plot the strength of the electric field as a function of position (z). Electric Field**Let’s do it backwards…**Electric Field**EXCEL**ETC …. Electric Field**??**alpha=1.89 Electric Field**The mystery solved!!!**BE CAREFULL! Electric Field**In the Figure, the four particles are fixed in place and**have charges q1 = q2 = +5e, q3 = +3e, and q4 = -12e. Distance d = 9.0 mm. What is the magnitude of the net electric field at point P due to the particles? Electric Field**Figure 22-34 shows two charged particles on an x axis, q =**-3.20 10-19 C at x = -4.20 m and q = +3.20 10-19 C at x = +4.20 m. (a) What is the magnitude of the net electric field produced at point P at y = -5.60 m?[7.05e-11] N/C(b) What is its direction?[180]° (counterclockwise from the positive x axis) Electric Field