西南交通大学：《大学物理》课程教学资源（讲稿，双语）CHAPTER 16 Electric Charges, Electrica Forces and lectric Fields

UNIVERSITY PHYSICS II CHAPTER 16 Forces and lectric Fields 8 16.1 Coulomb's force law for pointlike charges 1. The discovery of electrification OThe phenomenon of electrification Glass rod is rubbed with silk--positive Amber rod is rubbed with fur --negative ② electric charge is an intrinsic characteristic of the fundamental particles making up Neutral copper matters Charged plastic

1 1. The discovery of electrification 2electric charge is an intrinsic characteristic of the fundamental particles making up matters. 1The phenomenon of electrification Glass rod is rubbed with silk—positive Amber rod is rubbed with fur--negative §16.1 Coulomb’s force law for pointlike charges

816. 1 Coulomb's force law for pointlike charges Glass Plastic @like charges(charges with the same sign) repel each other and unlike charges(charges with opposite electrical signs)attract each other 8 16.1 Coulomb's force law for pointlike charges 2. The properties of electric charge Othe charges are scalar: @charges are quantization; e=1602177*10-1CgF=ne up quarks: 2e/3, down quarks: -e/3 Othe total amount of electric charges is conserved in any process involving an isolated system 3. The polarization and induction Why can comb rubbed with fur attract small pieces of paper?

2 3like charges(charges with the same sign) repel each other, and unlike charges(charges with opposite electrical signs) attract each other. §16.1 Coulomb’s force law for pointlike charges §16.1 Coulomb’s force law for pointlike charges 2. The properties of electric charge 1the charges are scalar; 2charges are quantization; e=1.602177*10-19C q=ne up quarks: 2e/3, down quarks: -e/3 3the total amount of electric charges is conserved in any process involving an isolated system. 3. The polarization and induction Why can comb rubbed with fur attract small pieces of paper?

816. 1 Coulomb's force law for pointlike charges 8 16.1 Coulomb's force law for pointlike charges insulator Electric dipole electrical polarization conductor induction grounding

3 §16.1 Coulomb’s force law for pointlike charges §16.1 Coulomb’s force law for pointlike charges + + + + + −−− − − − − −− − − + + +++ + ++ + + + −− − − − − − −− − − induction + + + + + grounding conductor induction + + +++ + electrical polarization insulator − + − + − + − + − + − + − + Electric dipole

816. 1 Coulomb's force law for pointlike charges 8 16.1 Coulomb's force law for pointlike charges A

4 §16.1 Coulomb’s force law for pointlike charges §16.1 Coulomb’s force law for pointlike charges

816. 1 Coulomb's force law for pointlike charges 4. Coulomb’ s force law ① Experiments: q Q心 (a)Repulse F∝ Q F 1 qe (b)Repulsion F qe Permitivity of free space (c) Attraction E0=8.854187817×10-C/(N·m) @mathematical expression F 4TEor2l 8 16.1 Coulomb's force law for pointlike charges @Compare Coulomb's law and universal gravitational force F 221 F=- r2 For two electrons n grav mCm2=417×1042

5 §16.1 Coulomb’s force law for pointlike charges 4. Coulomb’s force law 1Experiments: 2 1 r F ∝ 2 r q Q F ∝ 2 0 4 1 r q Q F πε = 8.854187817 10 C /(N m) 12 2 0 = × ⋅ − ε Permitivity of free space q q q Q Q Q 2 21 0 21 ˆ 4 1 r r qQ F πε = r 2mathematical expression 3Compare Coulomb’s law and universal gravitational force §16.1 Coulomb’s force law for pointlike charges 2 21 0 21 ˆ 4 1 r r qQ F πε = r 2 21 21 rˆ r mM F = −G r For two electrons: 2 2 0 elec 4 1 r e F πε = 2 2 grav r m F G e = − 42 2 2 grav 0 elec 4.17 10 4 1 = = × Gme e F F πε

§161 Coulomb’ s force law for pointlike charges 5. The principle of superposition The total electrical force on given charge is the vector sum of the electrical forces caused by the other charges, calculated as if each acted alone Fw=F1+F2+… Q Q3°F3F2 816.2 The electric field of static charge and electric field lines 1. The definition of electric field of static charge F at point electric field E qt The electric field at a point in space is the force per Coulomb RE at that point(N/C), direct the direction of force exerted on a positive test charge Electric field Test charge is small enough, does not alter the distribution of the charges creating the field 6

6 §16.1 Coulomb’s force law for pointlike charges 5. The principle of superposition The total electrical force on given charge is the vector sum of the electrical forces caused by the other charges, calculated as if each acted alone. L r r r Ftotal = F1 + F2 + q Q1 Q3 Q2 + + + − F1 r F3 r F2 r §16.2 The electric field of static charge and electric field lines 1. The definition of electric field of static charge test q F E r r electric field = Test charge is small enough, does not alter the distribution of the charges creating the field. The electric field at a point in space is the force per Coulomb at that point(N/C), direct the direction of force exerted on a positive test charge

816.2 The electric field of static charge and electric field lines Notice OThe electric field depends on the shape and the distribution of the charges @the gravitational force is always parrallel to the gravitational field in the gravitational case. but the electrical force can be either parallel or antiparallel to the electric field The force on a positive charge +q is parallel to the electric field. the force on a negative charge-g is antiparallel to the electric field F=gE 816.2 The electric field of static charge and electric field lines 2. The electric field of pointlike charge distribution Test F charge F 4兀E021 Q F10 For +O E q za q

7 Notice: 1The electric field depends on the shape and the distribution of the charges. 2the gravitational force is always parrallel to the gravitational field in the gravitational case, but the electrical force can be either parallel or antiparallel to the electric field. The force on a positive charge +q is parallel to the electric field, the force on a negative charge -q is antiparallel to the electric field. F qE r r = §16.2 The electric field of static charge and electric field lines §16.2 The electric field of static charge and electric field lines 2. The electric field of pointlike charge distribution Test charge r r F q r Q 2 21 0 21 ˆ 4 1 r r qQ F πε = r r r Q q F E ˆ 4 1 2 πε 0 = = r r r r Q q F E ˆ 4 1 2 πε 0 = = − r r For +Q For -Q

816.2 The electric field of static charge and electric field lines 3. The principle of superposition The total electric field at the point when all he pointlike charges are present simultaneously at their fixed position is the vector sum of the individual fields E F F2 +—2+…orE r4兀E0r E1+E2 4. Electric field lines A useful alternative geometric representation of electric field 816.2 The electric field of static charge and electric field lines The properties of the electric field lines: OThe electric field lines begin on positive charges and end on negative charges; The direction of the electric field at any point is tangent to the field line passing through that point and in the direction indicated by arrows on the field line 2The electric field is strong where field lines are close together and weak where they are far apart. The number of lines passing through square meter oriented perpendicular to the lines is proportional to the magnitude of the electric field 8

8 §16.2 The electric field of static charge and electric field lines 3. The principle of superposition The total electric field at the point when all the pointlike charges are present simultaneously at their fixed position is the vector sum of the individual fields. L r r L r r r r = + + = = + + 1 2 1 2 E E q F q F q F E 4. Electric field lines A useful alternative geometric representation of electric field. i i i i r r Q E ˆ 4 2 0 = ∑ πε r or 1The electric field lines begin on positive charges and end on negative charges; The direction of the electric field at any point is tangent to the field line passing through that point and in the direction indicated by arrows on the field line. The properties of the electric field lines: §16.2 The electric field of static charge and electric field lines 2The electric field is strong where field lines are close together and weak where they are far apart. The number of lines passing through a square meter oriented perpendicular to the lines is proportional to the magnitude of the electric field

816.2 The electric field of static charge and electric field lines 3 Field lines are never cross. The field at any point has a unique direction Examples: E1 816.2 The electric field of static charge and electric field lines

9 §16.2 The electric field of static charge and electric field lines Examples: 3Field lines are never cross. The field at any point has a unique direction. §16.2 The electric field of static charge and electric field lines

16. 3 The distribution of electric field and calculation 1. The electric field of the electric dipole l2 l2 F Electric dipole moment p=gd 816.3 The distribution of electric field and calculation @along the axis of the dipole y +oe a d/2 E-E+E-gI 4m6 -k (Z z十 2zd E 2 p z > 4z 10

10 1. The electric field of the electric dipole §16.3 The distribution of electric field and calculation − + d r p Q d r r = − Q + Q Electric dipole moment p Q d r r = k d z d z Q E E E ˆ] ) 2 ( 1 ) 2 ( 1 [ 4 2 2 0 + − − = + + − = πε r r r k d z Q zd ˆ ) 4 ( 2 4 2 2 0 2 − = πε 3 4 0 2 z p E πε r r = z >> d 1along the axis of the dipole §16.3 The distribution of electric field and calculation − Q + Q d 2 z E+ r E− r o A z y