Article 1 of AAA
Extended electromagnetic induction law
Abstract: Electromagnetic induction is one of the most important discoveries in electromagnetism, which reveals the interrelation between electric and magnetic phenomena. The significance of Faraday's law of electromagnetic induction lies in that on the one hand, according to the principle of electromagnetic induction, people have made generators, which makes it possible to generate electric energy on a large scale and transmit it over a long distance; On the other hand, electromagnetic induction is widely used in electrical technology, electronic technology and electromagnetic measurement. This paper understands and applies several expansions.
Keywords: extended understanding and application of electromagnetic induction law
Abstract: Electromagnetic induction is one of the most important discoveries in electromagnetism, which reveals the phenomenon between electricity and magnetism. The significance of Faraday's law to electromagnetic induction lies in that on the one hand, according to the principle of electromagnetic induction, people have made generators, making it possible to produce electricity on a large scale and transmit electricity over a long distance; On the other hand, electromagnetic induction is widely used in electrical technology, electronic technology and electromagnetic measurement methods. This paper will expand the understanding of several applications.
Keywords: electromagnetic induction law to expand the application of understanding
China Library Classification Number: O44 1.3 Document Identification Number: a document number:
Faraday's law of electromagnetic induction: the magnitude of induced electromotive force in a circuit is directly proportional to the rate of change of magnetic flux passing through the circuit. In order to generate induced electromotive force in the circuit, the magnetic flux in the circuit must be changed. The change of the magnetic induction intensity of the original magnetic field in the loop, the change of the loop area, and the simultaneous change of the original magnetic field and area will all cause the change of magnetic flux and produce the induced electromotive force. Here, the understanding and application of several expansions of Faraday's law of electromagnetic induction are discussed through concrete examples.
First, the change of magnetic flux is only due to the change of the original magnetic field with time, resulting in induced electromotive force.
Example 1. As shown in the figure, a square metal wire frame with a side length of L, a mass of M and a resistance of R is suspended on the edge of a bounded uniform magnetic field with thin wires. The upper part of the metal frame is inside the magnetic field, and the lower part is outside the magnetic field. The law of magnetic field changing with time is B = kt. It is known that the maximum tensile force that a thin thread can bear is 2mg, so how long does it take from t=0?
Answer: induced electromotive force
The induced current in the wireframe is:
There is a solution to disconnection:
Secondly, the change of magnetic flux is only caused by the change of the original magnetic field with the spatial position, thus generating induced electromotive force.
Example 2. A metal ring with mass m, diameter d and resistance r falls vertically in a large magnetic field. The distribution of magnetic field is shown in the figure. It is known that the vertical component of magnetic induction intensity By only changes with height, and its relationship with height y is by = B0 * * * 1+KY * * * * * where k is a proportional constant and K. 0***, where the magnetic field along the axis of the ring is always vertical upward, and the plane where the metal ring is located is always horizontal during the falling process, and the speed increases continuously, and finally it stabilizes at a certain value, which is called the closing speed. ask
The direction of induced current in the loop;
* * * 2 * * Closing speed of the ring.
Solution: * * *1* * According to Lenz's law, the direction of induced current is clockwise * * * looking down, and the magnetic flux of * * * * * 2 * * * ring when falling at Y height is
Let the closing speed be vm, and the change of magnetic flux in δ t time moving at this speed is
According to Faraday's law of electromagnetic induction, there are
The electric power of the induced current in the loop is
According to the law of energy conversion and conservation, the power of gravity to do work is as follows
solve
Thirdly, the change of magnetic flux is only caused by the change of area, thus generating induced electromotive force.
Example 3. There is a uniform magnetic field in the circular area with radius a, the magnetic induction intensity is B=0.2T, the magnetic field direction is perpendicular to the paper surface, the metal ring with radius b is placed concentrically with the magnetic field, and the magnetic field is perpendicular to the torus, where a=0.4m, b = 0.6m, the lamps L 1 and L2 are connected to the metal ring respectively, and the resistance of the two lamps is r0 = 2ω Ω, regardless of the wire resistance.
Today, the right semicircle OL2O' is rotated 90 degrees upward with MN as the axis. If the turnover angular velocity is 0, find the average power of L 1.
Solution: turn to 90? The time spent on the angle
Average induced electromotive force generated by loop
Average power of L 1
Fourthly, the change of magnetic flux is only caused by the conductor cutting the magnetic induction line. Generate induced electromotive force
Example 4. Two long parallel metal rails with a distance d=0.20m are fixed on the same horizontal plane and are in a uniform magnetic field in the vertical direction. The magnetic induction intensity of the magnetic field is B=0.2T, and two thin metal bars are horizontally placed on the rail to form a rectangular loop. The resistance of each thin metal bar is r = 0.25Ω, and the resistance of the rest of the loop can be ignored. As we all know, two thin metal rods translate in opposite directions along the track at a constant speed under the tension parallel to the track.
Analysis: When two metal bars slide at a uniform speed V, the induced electromotive force generated in each metal bar is as follows:
According to the ohm's law of closed circuit, the current intensity in the circuit is:
Due to the balance between tension and ampere force, the tension acting on each metal bar is
Substitute the above formula into the data to get n.
Five, the original magnetic field and area caused by the change of magnetic flux * * *, resulting in induced electromotive force.
Example 5. As shown in the figure, two parallel metal guide rails are fixed on a horizontal table, and the resistance per meter of each guide rail is r0 = 0.10Ω/m, the end points p and q of the guide rails are connected by wires with negligible resistance, and the distance between the two guide rails is l = 0.20m There is a time-varying uniform magnetic field perpendicular to the table. It is known that the relationship between magnetic induction intensity B and time t is B=kt, and the proportional coefficient K = 0.020 t/s. A metal rod with negligible resistance can slide on the guide rail without friction and keep perpendicular to the guide rail during the sliding process. At the moment of t=0, the metal rod is close to both ends of P and Q, and under the action of external force, the rod slides from rest to the other end of the guide rail with constant acceleration, and the ampere force on the metal rod at t=6.0s is calculated.
Solution: A represents the acceleration of the metal rod. At time t, the distance between the metal rod and the initial position is, at this time, the speed of the rod is the area of the loop formed by the rod and the guide rail, the induced electromotive force in the loop is =, the total resistance in the loop is R=2Lr0, and the induced current in the loop acts on the ampere force. The solution is F=, and the substituted data is F = 1.44× 6544.
Note: Please view all formulas and charts in the article in PDF format.
AAA article 2
Mechanical problems in electromagnetic induction
Abstract: Inquiry learning in the information age meets the requirements of the new curriculum and can cultivate students' ability to solve problems. In physics teaching in senior high school, it is particularly important for students to explore independently. Aiming at the mechanical problems in electromagnetic induction, the author expounds autonomous inquiry learning.
Keywords: independent inquiry learning of electromagnetic induction mechanics problems
2 1 century is an information age, an internet age and an era of constant knowledge innovation. The fundamental significance and value of education lies in cultivating students' innovative spirit, exploration ability and problem-solving ability, thus shaping students' positive, healthy and upward personality. Research-based learning just meets such educational requirements. Autonomous learning and cooperative inquiry enable students to experience the process of solving problems personally, which is conducive to students' in-depth understanding of knowledge, and at the same time helps students to develop, extend, change and master the concepts and laws they have learned.
1. Develop independent inquiry learning according to the age characteristics of senior high school students.
High school students in their youth no longer depend on their parents for everything. They have been able to distinguish right from wrong, and their sense of independence has begun to awaken. The expression of emotion tends to be independent gradually, the development of cognitive ability is close to maturity, the ability of logical and abstract thinking is constantly enhanced and improved, and logical thinking can be used independently when thinking and solving problems. Therefore, their curiosity, thirst for knowledge and sense of success become stronger.
2. Carry out inquiry learning in specific problems.
The requirements of the new curriculum standard: let students understand the research thinking and methods of physics, cultivate the study habit and ability of independent thinking, and attach importance to the teaching of concepts and laws. The ability of scientific independent inquiry and the understanding of scientific inquiry are formed in the process of students' inquiry learning, which requires organizing students to carry out inquiry learning. Teachers should make the most effective use of time, create situations in the classroom, create space and time for students to think, and let students actively participate in autonomous inquiry learning.
The learning process is the learner's own activity, and only by participating in the learning can the learned knowledge be more solid. In senior high school, students have a strong sense of autonomous learning, and their autonomous learning ability has been initially possessed, but teachers need to further improve it. The effect of autonomous learning depends on the guidance of teachers. Teachers should guide students to get in touch with new knowledge before learning new lessons, and make use of existing knowledge reserves to explore, personally unveil the mystery of knowledge and occupy the main position of learning in advance. In this way, when teachers and students enter the learning process together, students will no longer feel strange, but will be more able to integrate into classroom teaching, accept knowledge more easily and happily, and form a harmonious, equal and cooperative teacher-student relationship.
Next, I will start with the college entrance examination questions, select targeted examples, and through the analysis and exploration of the examples, let students perceive the intention of the college entrance examination proposition, analyze students' thinking of analyzing problems, and cultivate students' ability to solve problems.
2. 1 Mechanical problems in electromagnetic induction
Proposition intention: to examine the ability of understanding, reasoning and comprehensive analysis.
Example 1. As shown in figure 1, two parallel metal wires P and Q are connected by wires with negligible resistance. The distance between the two guide rails is l = 0.20m, and there is a uniform magnetic field that varies with time perpendicular to the desktop. It is known that the relationship between magnetic induction intensity B and time t is B=kt, and the proportional coefficient K = 0.020 t/s. A metal bar with negligible resistance can be placed on the guide rail, and it can be kept constant when sliding. When t=0, the guide rails are fixed on the horizontal workbench, and the resistance per m of each guide rail is r = 0.10Ω/m, and the metal rods of the guide rail are close to the ends of P and Q.. Under the action of external force, the constant acceleration of the rod begins to slide to the other end of the guide rail, and the ampere force on the metal rod at t=6.0s is calculated.
Independent investigation:
The idea to solve the problem is to use a to represent the acceleration of the metal rod. At time t, the distance from the metal rod to the initial position is L=at.
At this time, the speed of the rod v=at,
The area of the ring formed by the rod and the guide rail is S = Ll,
The induced electromotive force in the loop E=S+Blv.
B=kt。
==k
The total resistance of the loop R=2Lr,
The induced current in the loop I=,
Ampere force acting on the rod F=BlI,
The solution is F=t,
Substitute data, F= 1.44× 10N.
Summarize the law:
* * *1* * Method: Starting from the relationship between motion and force, Newton's second law and electromagnetic induction law are used to solve it.
* * * 2 * * Basic idea: force analysis → motion analysis → change trend → determination of motion process and final stable state → solution by Newton's second law equations.
* * * 3 * * Note the characteristics of amperes:
In fact, pure mechanical problems are only gravity, elasticity, friction, electromagnetic induction and ampere force. When ampere force changes with speed, some elasticity and corresponding friction force also change, which leads to the change of motion state of the object. Pay attention to the above connection when analyzing problems.
2.2 conductor bar cutting magnetic induction line problem
Generally, the movement of the conductor bar cutting the magnetic induction line has the following situations: uniform movement, constant force movement, constant power movement and so on. Now take the motion under the constant force as an example to analyze.
Example 2. As shown in Figure 2, a pair of parallel and smooth R rails are placed on the horizontal ground, the distance between the two rails is L=0.20m, and the resistance R =1.0Ω; There is a conductor bar resting on the track, perpendicular to the two tracks, and the resistance between the bar and the track can be ignored. The whole device is in a uniform magnetic field with magnetic induction intensity B=0.50T, and the direction of the magnetic field is perpendicular to the track surface. Now, with an external force F, pull the rod along the track direction to make it do uniform acceleration. The relationship between the measured force f and the time t is shown in fig. 3. Find the mass m and acceleration a of the rod.
Independent investigation:
Analysis: the conductor bar moves in a straight line at a uniform speed on the track. V represents its speed, t represents time, and then V = at.
When the rod cuts the magnetic induction line, it will produce induced electromotive force E=BLv ②.
A current I=E/R③ is generated in the closed loop of rod, track and resistor.
The ampere force on the rod is F=IBL ④.
According to Newton's second law, there is F-F=ma⑤.
Combining the above types, F=maat ⑥ is obtained.
Substituting the points on the graph into Equation 6, we can get a= 10m/s and m=0. 1kg.
Summarize the law:
Under the action of constant external force, the conductor bar starts to move from rest, the speed increases, and the induced electromotive force increases continuously. Ampere force and acceleration are related to speed. When ampere force is equal to constant force, acceleration is equal to zero, and the conductor bar finally moves at a uniform speed. The acceleration of the whole process is variable, so the kinematic formula cannot be applied.
2.3 Comprehensive application of electromagnetic induction and circuit law
Example 3. The magnetic induction intensity of uniform magnetic field is B=0.2T, the magnetic field width is L=3rn, the side length of square metal frame is ab= 1m, and the resistance of each side is r = 0.2Ω. The metal frame passes through the magnetic field at a uniform speed of v= 10m/s, and its plane is always perpendicular to the direction of the magnetic induction line. As shown in Figure 4, find:
* * *1* * Draw the I-t diagram when the induced current passes through the magnetic field area in the metal frame;
* * * 2 * * Draw a U-t diagram of the voltage across ab.
Independent investigation:
Analysis: E=BLv=2V, I==2.5A When the wireframe enters the magnetic field,
The direction is counterclockwise, as shown by the solid line abcd in the figure, and the duration of the induced current is t = 0.1s.
When the wireframe moves in the magnetic field: E=0, I=0,
No-current duration: t==0.2s,
E=BLv=2V and I = I==2.5A when the wireframe passes through a magnetic field.
The direction of this current is clockwise, as shown by the dotted line abcd in Figure 4, and the counterclockwise current is positive, and the I-t diagram is shown in Figure 5.
* * * 2 * * The voltage at both ends of the wire frame entering the magnetic field area ab: U = IR = 2.5× 0.2 = 0.5V 。
When the wire frame moves in a magnetic field, the voltage across B is equal to the induced electromotive force:
U=BLv=2V。
When the magnetic field is generated from the wire frame, the voltage across ab is u = e-IR =1.5v. 。
The resulting U-t diagram is shown in figure 6.
* * *1* * circuit problem
① Determination of power supply: firstly, determine the conductor part that causes electromagnetic induction * * * power supply * * *, then use E=n or E=BLvsinθ to find the magnitude of induced electromotive force, and use right-hand rule or Lenz's law to determine the current direction.
② Analyze the circuit structure and draw the equivalent circuit diagram.
(3) Using circuit laws, mainly Ohm's law, series-parallel law, etc.
* * * 2 * * Image problem
① Qualitative or quantitative expression of the functional relationship of the studied problem.
② The directions of physical quantities such as E, I and B in the image are reflected by positive and negative values.
③ Pay attention to the definition or expression of unit length of abscissa and ordinate when drawing images.
The motion process of wireframe is divided into three stages. The first stage ab is the external circuit, the second stage ab is equivalent to the power supply when the circuit is open, and the third stage ab is the power supply connected to the external circuit.
In short, in physics teaching in senior high school, teachers should guide students to carry out independent inquiry learning, start with the college entrance examination questions, let students analyze and explore examples independently, guide students to sum up the rules, let students perceive the intention of the college entrance examination questions, analyze their thinking of analyzing problems, and then cultivate their ability.