Review basic knowledge points of engineering electromagnetic field

Chapter one Vector analysis and field theory 1 Source point refers to . 2 Field point refers to . 3 The distance vector is , The unit vector representing its direction is expressed by Express . 4 The isosurface equation of scalar field is expressed as , The vector line equation can be expressed in coordinate form , It can also be expressed in vector form . 5 Gradient is a tool for studying scalar fields , Modular representation of gradient , The direction of the gradient indicates . 6 The relationship between directional derivative and gradient is .

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Chapter two electrostatic field

1 Point charge q The formula for calculating the electric field intensity generated in space is .

2 Point charge q The calculation formula of the potential generated in space is .

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6 A conductor in static equilibrium , The direction of the electric field intensity on the surface of the conductor follows .

7 A conductor in static equilibrium , The electric field intensity inside the conductor is equal to .

8 A conductor in static equilibrium , The relationship between internal potential and external potential is .

9 A conductor in static equilibrium , Its internal charge volume density is .

10 A conductor in static equilibrium , The charge is distributed on the surface of the conductor .

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17 Volume density of polarized charge in medium

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20 Potential shift vector D, Electric field intensity vector E The relationship between is .

21 Dielectric strength refers to .

22 In electrostatic field , The curl of the electric field intensity is equal to .

23 In electrostatic field , The divergence of the electric displacement vector is equal to .

24 In electrostatic field , The line integral of the electric field intensity along any closed path is equal to .

25 In electrostatic field , The flux of the electric displacement vector on any closed surface is equal to .

26 In electrostatic field , The interface condition of electric field strength is .

27 In electrostatic field , The interface condition of the electric displacement vector is .

28 In electrostatic field , The Poisson equation satisfied by the potential is .

29 In electrostatic field , The interface condition satisfied by the potential is .

30 In electrostatic field , The normal derivative of potential at the interface of two media satisfies .

31 In electrostatic field , The tangential derivative of the potential at the interface between the two media satisfies .

32 In electrostatic field , The normal derivative of potential on the interface of conductor and medium satisfies .

33 In electrostatic field , The tangential derivative of potential at the interface of conductor and medium satisfies .

34 The first kind of boundary condition in electrostatic field boundary value problem is .

35 The second kind of boundary condition in electrostatic field boundary value problem is .

36 The third kind of boundary condition in electrostatic field boundary value problem is .

37 Elementary charge dq The formula for calculating the electric field intensity generated in space is .

38 Elementary charge dq The calculation formula of the potential generated in space is .

39 The differential form of the basic equation of electrostatic field is .

40 The boundary value problem of electrostatic field refers to .

The third chapter Constant electric field

1 The unit of Bulk current density is .

2 The unit of surface current density is .

3 The relationship between bulk current density and charge velocity is .

4 The relationship between surface current density and charge velocity is .

5 The relationship between current density and electric field intensity is .

6 The definition of external electric field is .

7 The definition of power electromotive force is .

8 The mathematical expression of the integral form of the current continuity equation is .

9 The mathematical expression of the differential form of the current continuity equation is .

10 The mathematical expression of the integral form of the current continuity equation in a constant electric field is .

11 The mathematical expression of the differential form of the current continuity equation in a constant electric field is .

12 The basic equation of constant electric field is .

13 The auxiliary equation of constant electric field is .

14 The differential form of Ohm's law is .

15 The relationship between electric field intensity and potential of constant electric field is .

16 The equation satisfied by the constant electric field potential outside the power supply is .

17 On the interface of two conductive media in a constant electric field , The interface condition of current density is .

18 In a constant electric field, when the conductivity of the conductive medium is known , On the interface , The interface condition satisfied by the normal derivative of potential is .

Chapter four Constant magnetic field

1 Volume current element 、 Area current element and line current element are respectively expressed as 、 、 .

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10 The Coulomb specification is expressed as .

11 Surfaces S The magnetic flux on the surface is Flux of , Expressed as .

12 The formula for calculating magnetic flux with vector magnetic potential is .

13 The continuous differential of magnetic flux is expressed as .

14 The magnetic induction line equation is expressed in the form of coordinates , Expressed as a vector, the form is .

15 In a parallel plane field , Magnetic induction line is .

16 The curl of magnetic induction intensity is equal to .

17 The radius is R There is current in the straight wire of I, The current is evenly distributed , The magnetic induction intensity inside the conductor is , The external magnetic induction intensity is .

18 There is current distribution on the infinite plane , Current area density K Is a constant vector , The magnetic induction intensity on both sides of the plane is .

19 A magnetic dipole is a small enclosed current carrying circuit , Set the loop area as S, The loop current is I, Then the magnetic dipole moment of the magnetic dipole m= .

20 Magnetization M The physical meaning of is .

21 Bulk density of magnetizing current JM= .

22 Area density of magnetizing current KM= .

23 Magnetic field intensity H, Magnetic induction intensity B, Magnetization M The relationship between .

24 For linear 、 Isotropic medium , Magnetic field intensity H And magnetic induction B The relationship between .

25 The differential form of the basic equation of the constant magnetic field is .

26 The auxiliary equation of the constant magnetic field is .

27 The interface condition of magnetic induction intensity is .

28 The interface condition of magnetic field strength is .

29 When there is no free current on the interface , The interface condition of magnetic field strength is .

30 The curl of the magnetic field intensity is equal to .

31 The line integral of the magnetic field intensity along any closed loop is equal to that around the loop .

32 The Poisson equation of vector magnetic potential is .

The fifth chapter Time varying electromagnetic field

1 The essence of Faraday's law of electromagnetic induction is the generation of a changing magnetic field .

2 Transformer electromotive force refers to .

3 Electromotive force of generator refers to .

4 The electric field generated by the changing magnetic field is called the induced electric field , The curl of the induced electric field is equal to .

5 Displacement current density is defined as JD= .

6 There are three forms of current , Respectively , , , The corresponding current density forms are , , .

7 The essence of the displacement current hypothesis is the generation of a changing electric field .

8 The differential form of the law of total current is .

9 Write the integral form of Maxwell's equations and its auxiliary equations .

10 Write the differential form of Maxwell's equations and its auxiliary equations .

11 The refraction law of electric field intensity on the interface of two media is .

12 The refraction law of the magnetic field intensity on the interface between two media is .

13 Write the differential form of Maxwell's equations in vector form and its auxiliary equations .

Chapter six Mirror method

1 The theoretical basis for implementing the mirror image method is .

2 In the process of implementing the image method , What cannot be changed is , ,

, What can be changed is , .

3 Write down the steps to implement the mirror method .

4 Above an infinite conductor h There is a little charge at q, Then the electric field intensity at any point in the upper half space is .

5 Above an infinite conductor h There is a little charge at q, The distribution law of electric field intensity on the surface of conductor is .

6 Above an infinite conductor h There is a little charge at q, The distribution law of the area density of the induced charge on the surface of the conductor is .

7 The boundary potential of the rectangular region is 0, The distance from a point charge to the two boundaries is a,b, Take the rectangular region as the region for solving the electric field , Write the mirror charge .

8 The radius of grounding conductor ball is R, Ball outer distance ball center d There is a little charge at q, Take the outside of the conductor sphere as the solution space , Then mirror charge q’= , Distance from the ball center .

9 The radius of grounding conductor ball is R, Ball outer distance ball center d There is a little charge at q, Then the electric field intensity outside the conductor is .

10 The radius of grounding conductor ball is R, Ball outer distance ball center d There is a little charge at q, Then the upper distance of the conductor sphere q The electric field intensity at the nearest point is , distance q The electric field intensity at the farthest point is .

11 The radius of grounding conductor ball is R, Ball outer distance ball center d There is a little charge at q, Then the induced charge surface density on the conductor sphere is .

12 The radius of ungrounded conductor ball is R, Ball outer distance ball center d There is a little charge at q, Then the conductor spherical potential is .

13 From the infinite dielectric interface h Place a little charge at q, The point charge is in the first medium , The dielectric constants of the two media are

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, Take the first medium as the solution region , Then the mirror charge is , Position in , The electric field intensity at any point in the upper half space is .

14 From the infinite dielectric interface h Place a little charge at q, The point charge is in the first medium , The dielectric constants of the two media are

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, Take the second medium as the solution region , Then the mirror charge is , Position in , The electric field intensity at any point in the lower half space is .

Chapter viii. Energy and force of electromagnetic field

1 It is known that n The charge of each conductor is

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, Potential

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, The electric field energy of the electrostatic system is .

2 The potential shift vector of the known electric field D And electric field strength E, Then the volume density of the electric field energy distribution is .

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6 The magnetic induction intensity of a known magnetic field B And magnetic field strength H, Then the volume density of the magnetic field energy distribution is .

7 Poyinting vector Sp= , Physical meaning .

8 When the potential remains constant , About generalized coordinates g Generalized electric field force fg= , When the power remains unchanged , About generalized coordinates g Generalized electric field force fg= .

9 When the current is constant , About generalized coordinates g Generalized magnetic force fg= , When the flux linkage does not change , About generalized coordinates g Generalized magnetic force fg= .

10 When the generalized coordinates are angles , The generalized force calculated by the virtual displacement method is .

Chapter nine Plane electromagnetic wave

1 The uniform plane electromagnetic wave in infinite ideal medium is TEM wave , The direction of the electric field 、 The relationship between the direction of magnetic field and the direction of wave propagation is .

2 The ratio of electric field strength to magnetic field strength of uniform plane electromagnetic wave in ideal medium is .

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5 The wave impedance of vacuum medium is .

6 It is proved that the electric field energy density of plane electromagnetic wave in ideal medium is equal to the magnetic field energy density .

7 The phase relationship between the electric field intensity and the magnetic field intensity of plane electromagnetic waves in an ideal medium is .

8 The frequency is f, The speed of propagation is v The plane electromagnetic wave propagates in the ideal medium , The phase constant is , Its physical meaning is .

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16 Penetration depth is defined as , The relationship with attenuation constant is .

17 The relationship between attenuation constant and phase constant in a good conductor is .

18 The penetration depth of electromagnetic wave in a good conductor is

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, therefore , For high-frequency electromagnetic waves , Electromagnetic fields can only exist in the , This phenomenon is called .

Chapter ten Calculation principle of circuit parameters

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