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Comprehensive knowledge of electromagnetic induction

Source:百家号Publisher:小陈电子 Keywords: Electromagnetic induction Updated: 2023/07/14

1. The direction of the magnetic field generated by an energized wire

1. Magnetic field and magnetic field lines

The current-carrying wire can attract the deflection of the small magnetic needle, indicating that there is a special substance around the moving charge, called a magnetic field. The magnetic field has two characteristics: ① It has a force on magnets, moving charges and energized conductors; ② It has energy and can do work on moving energized conductors.

The small magnetic needles are connected with smooth curves in the direction pointed by the N pole at each point in space, and a series of curves can be obtained. These curves are called magnetic induction lines or magnetic induction lines.

2. Judgment of magnetic field direction

(1) The direction of the magnetic field around a straight energized wire

The magnetic field lines around a straight current-carrying wire are a series of concentric circles with the wire as the center. The closer to the wire, the stronger the magnetic field and the denser the magnetic field lines. The direction of the magnetic field is determined by the right-hand rule, as shown in the figure.

right hand rule for straight conductors

right hand rule for straight conductors

(2) The direction of the magnetic field in the energized wire frame

In the energized single-turn wire frame, there is a magnetic field both inside and outside the frame, and the direction of the magnetic field inside the frame is opposite to the direction of the magnetic field outside the frame. Use your right hand when judging the direction of the magnetic field within the box, as shown in the figure.

Wireframe right hand rule

Wireframe right hand rule

(3) The direction of the magnetic field of the energized solenoid

Use your right hand to judge the N pole of the solenoid. As shown in the figure, the direction in which the four fingers are bent is the current direction of the solenoid wire, and the end pointed by the thumb is the N pole of the solenoid.

Solenoid right hand rule

Solenoid right hand rule

2. The force exerted by the energized wire in the magnetic field

The direction of the force exerted on a current-carrying wire in a magnetic field can be determined by the left-hand rule; extend your left hand so that your thumb is perpendicular to the other four fingers, and the thumb and four fingers are in the same plane. Let the magnetic field lines pass vertically through the palm of your hand. The direction pointed by the four fingers is the direction of the current in the wire, and the direction pointed by the thumb is the direction in which the current-carrying wire is acted upon by the magnetic field, as shown in the figure.

left hand rule

left hand rule

When the direction of the current in the wire is perpendicular to the direction of the magnetic field, the force exerted on the wire is:

The force exerted on a wire in a magnetic field

The force exerted on a wire in a magnetic field

When the angle between the current direction in the energized wire and the magnetic field lines is θ, the force exerted on the wire is:

The force exerted on a wire in a magnetic field

The force exerted on a wire in a magnetic field

The direction of the resultant force of a current-carrying conductor in a magnetic field


The direction of the resultant force of a current-carrying conductor in a magnetic field

3. Physical quantities describing magnetic fields

1.Magnetic induction intensity

At a certain point in the magnetic field, the ratio of the force F on a straight energized wire perpendicular to the direction of the magnetic field to the product of the length L of the energized wire and the current I is called the magnetic induction intensity at this point.

The magnetic induction intensity is represented by the symbol B, then

Magnetic induction intensity calculation formula

Magnetic induction intensity calculation formula

2.Magnetic flux

The straight line that is perpendicular to the plane and leaves the plane is called the normal of the plane, as shown in the figure.

Magnetic flux passing through a closed coil

Magnetic flux passing through a closed coil

In a uniform magnetic field, the product of the area S of the plane perpendicular to the direction of the magnetic field and the magnetic induction intensity B is called the magnetic flux passing through this plane. The universal magnetic symbol Φ represents, then

magnetic flux

magnetic flux

If the angle between the normal line of the plane and the magnetic field lines is θ, the magnetic flux passing through the plane is:

magnetic flux

magnetic flux

4. Law of electromagnetic induction

1. Electromagnetic induction phenomenon

As shown in the figure, when the wire cuts the magnetic field line in the magnetic field or the magnetic flux passing through the coil changes, an induced electromotive force is generated; when the induced electromotive force is connected to the circuit to form a closed loop, there is current in the circuit. This phenomenon It's called electromagnetic induction. The current formed by electromagnetic induction is called induced current.

Several situations that produce electromagnetic induction

Several situations that produce electromagnetic induction

2. The size of the induced electromotive force

The magnitude of the induced electromotive force is proportional to the number of turns of the coil and the rate of change of the magnetic flux passing through the coil. This is Faraday's law of electromagnetic induction.

The induced electromotive force is represented by the symbol e, the number of turns of the coil is represented by the symbol N, and the rate of change of the magnetic flux passing through the coil is represented by the symbol ΔΦΔt. Then the magnitude of the induced electromotive force is:

induced electromotive force

induced electromotive force

It is usually agreed that the direction of the magnetic flux Φ element that causes the induced electromotive force is the reference direction. The direction of the induced electromotive force e and the direction of the Φ element follow the right-hand spiral rule, as shown in the figure.

right hand rule

right hand rule

The direction pointed by the thumb represents the direction of the magnetic flux Φ that causes the induced electromotive force, and the direction in which the four fingers are bent represents the reference direction of the induced electromotive force e. This is the right-hand spiral rule.

3. Direction of induced electromotive force

(1) The direction of the induced electromotive force generated by the conductor cutting the magnetic field lines

When a conductor cuts a magnetic field line, the direction of the induced electromotive force and induced current is determined by the right-hand rule, as shown in the figure.

right hand rule

right hand rule

(2) Use Lenz’s law to determine the direction of induced electromotive force

The magnetic field generated by the induced current always hinders the change of the magnetic field causing the induced current. This is Lenz's law.

The methods and steps for determining induced electromotive force using Lenz's law are as follows:

First determine how the direction and strength of the magnetic field causing the induced current changes; determine the direction of the magnetic field generated by the induced current according to Lenz's law; use the right-hand rule to determine the direction of the induced current; according to whether the induced current flows from the negative pole to the positive pole in the conductor or coil The principle determines the direction of the induced electromotive force. When the coil L1 is connected to the power supply and the switch S is closed, the direction of the magnetic field of the coil L1 is shown in Figure (b), and the magnetic field also passes through the coil L2. When the sliding contact D of the sliding resistor RP slides to the left, the current in the coil L1 increases, thus causing the magnetic field of the induced current to increase.

According to Lenz's law, when the magnetic field causing the induced current increases, the direction of the magnetic field produced by the induced current is opposite to the direction of the magnetic field causing the induced current. Therefore, the direction of the magnetic field generated by the induced current is shown by the dotted line in figure (c).

Use the right-hand rule to determine the direction of the induced current in coil L2. As shown in Figure (d), it flows from the P terminal to the Q terminal in the coil L2.

According to the induced current flowing from the negative pole of the induced electromotive force to the positive pole in the coil, it is judged that the direction of the induced electromotive force in the coil L2 is from P to Q, that is, P is the negative pole and Q is the positive pole.

Determine the direction of induced electromotive force

Determine the direction of induced electromotive force

5. Summary

Although magnetic fields may not play a big role in some circuit designs, EMI and EMC in PCB design are of great help, and these contents are useful in wireless charging circuits. The more you know, the better you will be at designing. There is no end to learning.


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