A physical property of matter. There are two kinds of charges in nature, namely positive charge and negative charge. Charged objects are called charged objects. Charge does not refer to electrons or protons, but electrons have negative charge, and protons have negative charge. with positive charge

Physics dictates: A glass rod rubbed with silk has a positive charge, and a rubber rod rubbed with fur has a negative charge.

Basic properties of charged bodies: attracting light and small objects The law of interaction between charges: like charges repel each other and dissimilar charges attract each other

Point charge: When the size and shape of the charged body itself have little impact on the research problem, the charged body can be regarded as a point charge

Elemental charge: e=1.6×10⁻¹⁹C. The charge of all charged objects is an integer multiple of the elemental charge. The charges of protons and positrons are the same as the elemental charge. The amount of charge was measured by the American physicist Millikan through the oil drop experiment. The element charge is the smallest amount of charge. The elemental charge is not charged iron. It is a numerical value, which is the absolute value of the charge of an electron or a proton. It is neither a proton nor an electron.

electrostatic field

Content: Charge will neither be created nor disappear out of thin air. It can only be transferred from one object to another object, or from one part of an object to another part; during the transfer process, the total amount of charge remains unchanged. Another way to express it: a system with no charge exchange with the outside world, the algebraic sum of charges remains unchanged

The neutralizing essence of the phone: the combination of positive and negative charges, the stable system composed of positive and negative charges (nucleus and electrons) (electrons moving around the nucleus)

Starting point

Essence: The essence of an object being charged is that the transfer (gain and loss) of electrons shows a net charge, thus showing electrical properties. During the process of charge separation, combination, and transfer, the algebraic sum of charges remains unchanged.

Content: The interaction force between two stationary point charges in a vacuum is proportional to the product of their charges and inversely proportional to the square of their distance. The direction of the force is on the line connecting them.

Expression: F=k(q₁·q₂)/r² k is the electrostatic force constant, k=9.0×10⁹N·m²/C² r is the distance between two point charges q₁, q₂ are the charges of two point charges

Coulomb's law was studied by Coulomb through the torsion balance, and k was calculated by later generations based on Maxwell's equations.

Applicable conditions: stationary point charges in vacuum (1) In air, the force between two point charges is approximately equal to that in vacuum. The formula can be directly applied (2) When the distance between two charged objects is much larger than their own size, the charged objects can be regarded as point charges.

The Coulomb force between two charged bodies is a pair of action force and reaction force. When calculating, the absolute value of the charge is generally substituted into the calculation size, and then judged based on "like charges repel each other, and dissimilar charges attract each other" direction of force

In contact electrification, for two identical conductors, if they both carry the same charge before contact, then they will share the total charge equally after separation; and if they both carry the same charge before contact, they must be neutralized first. After summing, the remaining charge is divided equally.

For two identical conductors, the process of multiple contacts will re-divide the total charge equally.

For two uniformly charged insulating spheres, they can be regarded as point charges with charges concentrated at the center of the sphere, and r is the distance between the sphere centers.

For two charged conductors, it is necessary to consider the phenomenon of uneven charge distribution on the charged body caused by electrostatic induction. Coulomb's law cannot be used directly for quantitative calculation, but Coulomb's law can be used to make quantitative judgments. Similar charges repel each other: F＜k(q₁·q₂)/r² Different charges attract each other: F>k(q₁•q₂)/r²

Balance condition: The combined field strength of two point charges at the third point charge is zero, or the two Coulomb forces on each point charge must be equal in magnitude and opposite in direction.

law of balance

Charge distribution law: √q₁q₃=√q₁q₂ √q₂q₃

Under the action of Coulomb force, the balance problem of charges is the same as the balance problem of objects in mechanics.

When two charged bodies move relative to each other, the magnitude of the Coulomb force changes as the distance between the charged bodies changes. As the movement occurs and proceeds, the force situation of the charged body changes, and the force situation will in turn affect the state of motion. Therefore, the characteristic of this type of problem is that force and movement restrict each other. In this case, the charged body The key to solving this kind of problem is the movement of variable acceleration. It is to use Cow's second law to analyze clearly the relationship between motion and force.

There is no relative motion between the two charged bodies. At this time, the Coulomb force is a constant force. In this case, the charged body usually moves in a straight line at a uniform speed. In this case, the "whole method" and "isolation method" can be used to analyze the force and motion of the charged body.

Variable acceleration motion involves the problem of dynamic critical value, that is, usually the speed takes the maximum value when the acceleration is zero. Whether it is the maximum value or the minimum value depends on the motion state of the object at the initial moment and the relationship between the subsequent motion and the force. relation

Definition: An electric field is a special objective substance that exists around charges and can transmit interactions between charges. The concept of "field" was first proposed by Faraday.

Basic properties: It has a powerful effect on the charges placed in it. The force of the electric field on the charges is called the electric field force.

The interaction between charges is accomplished by an electric field

As long as an object is charged, there must be an electric field in the space around it

Electric field strength: The ratio of the electric field force F experienced by a test charge placed at a certain point in the electric field to the amount of charge q it carries is called the electric field strength at that point, or field strength for short, represented by the letter E.

Definition formula: F=F/q (applicable to all electric fields)

Unit: In the International System of Units, it is Newton/column (N/C), Volt/meter (V/m)

Field strength is a physical quantity defined by the ratio definition method. Its size has nothing to do with the physical quantities F and q used to define it. It is just numerically equal to F/q (when using this formula to calculate field strength, F and q both refer to absolute value), its magnitude is determined by the electric field itself

Physical meaning: used to characterize the ability of an electric field to exert a force on a charge

Absoluteness: When the original charge of the field is determined, the field strength and direction of each point in space are determined.

Field strength is a vector, which stipulates that the direction of the field strength at a certain point in the electric field is the same as the direction of the electric field force experienced by positive charges at that point, and opposite to the direction of the electric field force experienced by negative charges at that point.

The direction of the field strength can be determined from the properties of the electric field lines If the electric field line is a straight line, then the direction of the field strength at a certain point on the electric field line is the direction pointed by the electric field line; If the electric field line is a curve, then the tangent direction at a point on the curve represents the direction of the field strength at that point

Expression: E=kQ/r² Q is the charge quantity of the field source charge r is the distance from the point to the field source charge

Direction: When the field source charge is a positive charge, the field strength direction of a certain point is away from the field source charge along the point and the field source charge; when the field source charge is a negative charge, the field strength direction of a certain point is along the line with the field source charge. The line points to the field source charge

Applicable conditions: (1), vacuum (2), stationary point charge

Calculation method

Compare

Principle: The electric field strength at a certain point in the electric field is equal to the vector sum of the field strengths generated at that point when all point charges around the point exist alone.

The superposition of vector sums of field strengths follows the parallelogram rule for vectors

Equivalent method Transform complex electric field scenarios into simple or familiar electric field scenarios while ensuring the same effect

Symmetry The electric field formed by using symmetrically distributed charges in space has the characteristics of symmetry

Micro-element method Divide the charged body into many tiny units, use the point charge field strength calculation formula to find the field strength of a certain micro unit, and then use the symmetry method to superimpose the field strengths of each micro circle to find the field strength of the charged body.

compensation law Establish a physical model based on the conditions given in the problem

Extreme hypothesis method (qualitative analysis of field strength distribution characteristics)

Electric field lines start from a positive charge, or infinity, and end at infinity, or a negative charge

Electric field lines do not intersect, are not tangent, and are not closed in the electric field

In the same electric field, the electric field intensity is greater where the electric field lines are denser; where the electric field lines are sparser, the electric field intensity is smaller.

The tangent direction of a point on the electric field line represents the direction of the electric field intensity at that point

The electric potential gradually decreases along the direction of the electric field line

Electric field lines and equipotential surfaces are perpendicular to each other where they intersect

Determine the direction of the electric field intensity: the tangent direction of any point on the electric field line is the direction of the electric field at that point

Determine the direction of the electric field force: the force direction of the positive charge is the same as the tangent direction of the electric field line at that point, and the force direction of the negative charge is opposite to the tangent direction of the electric field line at that point.

Determine the intensity of the electric field (qualitative): The intensity of the electric field is large where the electric field lines are dense, and the intensity of the electric field output by the electric field lines is small. This can then be used to determine the magnitude of the force and acceleration of the charge.

Determine the level of the electric potential and the speed of the electric potential decrease: the electric potential gradually decreases along the direction of the electric field line, and the direction of the electric field intensity is the direction in which the electric potential decreases fastest.

point charge

Two equal charges

Electric field lines for other common electric fields

The relationship between field strength, electric field force, acceleration and electric potential can be judged by the density of the electric field lines.

The magnitude of electric potential energy and kinetic energy, as well as the positive and negative aspects of work, need to be judged by providing functional relationships, kinetic energy theorem, and energy conservation. If the charged particle is only affected by the electric field force during motion, the total amount of electromotive force and kinetic energy of the particle remains unchanged, the electric field force does positive work, the kinetic energy increases, and the electric potential energy decreases

When a charged particle makes a curved motion in an electric field, since the direction of the resultant force points to the concave side of the trajectory, the direction of the electric field or the direction of the particle's electric and sexual field strength can be determined.

Draw the "velocity line" (the tangent line of the motion trajectory at the initial position) and the "force line" (the tangent direction of the electric field line at the initial position), and analyze the changes in the particle speed from the angle between the two.

"Classification discussion of the three unknown times": the positive and negative of the charge, the direction of the field strength or the level of the potential of the equipotential surface, the direction of the charge movement, or any one of them is known, and the various quantities to be determined can be analyzed in sequence; if If you don’t know all three, you have to use the hypothetical method to discuss each situation separately.

The ratio of the electric potential energy of charges at a certain point in the electric field to their charge amount

Definition: φ=Ep/q

Off-scale: The electric potential is a scalar quantity, which can be divided into positive and negative. Its positive (negative) means that the TV at this point is higher (lower) than the zero potential point.

Relativity: Electric potential is relativistic. The electric potential at the same point is different depending on the zero potential point. Usually the electric potential at infinity or the earth is zero.

The electric field force that moves the charge between any two points on the same equipotential surface does no work.

The equipotential surface must be perpendicular to the electric field lines, that is, perpendicular to the direction of the electric field intensity.

Electric field lines always point from an equipotential surface with a higher electric potential to an equipotential surface with a lower electric potential.

Where the arithmetic equipotential surfaces are denser, the electric field intensity is greater, and conversely, the electric field intensity is smaller.

Definition: The potential energy of a charge at a certain point in the electric field is equal to the work done by the electric field force when moving the charge from that point to the zero potential point.

The relationship between the work done by the electric field force and the change of the electric potential energy: the work done by the electric field force is equal to the reduction of the electric potential energy

Qualitative analysis

Quantitative calculation