# AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班 M Sittig Ch 20: Electrostatics.

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AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班 M Sittig Ch 20: Electrostatics

Apologies  Electricity (and magnetism) is a huge topic and we’re going to go quickly, learning just enough to score a 5 on the AP Exam.  If you take a full-year class, you will get a better, fuller picture that is not possible now due to time restraints.

Electric Charge  The forces between electric charges hold the world together.  But we rarely notice them because, unlike gravity, electric particles come in positive and negative, so they mostly cancel out across large distances.

Electric Charge  Charge is a property of matter, like mass.  Three charged particles: + (protons), – (electrons) and neutral (neutrons).  Our bodies, for example, contain a huge amount of protons, but also a huge amount of electrons.  So on a large scale, most objects are neutral.  Charge is measured in Coulombes (C).  Charge of an electron is 1.6×10 -19 C.

ConcepTest 16.1aElectric Charge I ConcepTest 16.1a Electric Charge I 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?

ConcepTest 16.1aElectric Charge I ConcepTest 16.1a Electric Charge I same charge The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative. 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? Follow-up: What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral?

1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) From the picture, what can you conclude about the charges? ConcepTest 16.1bElectric Charge II ConcepTest 16.1b Electric Charge II

1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) From the picture, what can you conclude about the charges? The GREEN and PINK balls must have the same charge, since they repel each other. The YELLOW ball also repels the GREEN, so it must also have the same charge as the GREEN (and the PINK). ConcepTest 16.1bElectric Charge II ConcepTest 16.1b Electric Charge II

Interaction between Charges  Opposite charges attract (attractive force).  Like charges repel (repulsive force).  Using charge to create “induced charge”: (Object is still net neutral. Balloon on wall demo.)

Electrons and Protons  Protons are stuck in the nucleus, don’t move.  Electrons are freer to move/flow, especially in metals.  Metals are good conductors = electrons can flow through them.  Materials that don’t conduct electrons = insulators.

Interaction between Charges  Like charges on a conductor will move as far away from each other as possible.  Charges will stay on the surface of conductors.  Charges will collect on sharp points and edges.

ConcepTest 16.2aConductors I ConcepTest 16.2a Conductors I 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be:

negative neutral induction Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction. 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be: remember the ball is a conductor! ConcepTest 16.2aConductors I ConcepTest 16.2a Conductors I Follow-up: What happens if the metal ball is replaced by a plastic ball?

Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? ConcepTest 16.2bConductors II ConcepTest 16.2b Conductors II 1)00 2)+– 3)–+ 4)++ 5)– – 0 0 ? ?

positive charge will flow from the blue to the green ball due to polarization charges will remain on the separate conductors While the conductors are connected, positive charge will flow from the blue to the green ball due to polarization. Once disconnected, the charges will remain on the separate conductors even when the rod is removed. Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? ConcepTest 16.2bConductors II ConcepTest 16.2b Conductors II 1)00 2)+– 3)–+ 4)++ 5)– – 0 0 ? ? Follow-up: What will happen when the conductors are reconnected with a wire?

Electric Fields  Fields were invented to explain how objects could interact without “touching”.  Objects with mass have gravitational fields, other masses in the field interact and feel a gravitational force.  Objects with (electric) charge have electric fields, other charges in the field interact and feel an electric force.

Electric fields  Electric fields are vector fields: each point in the field has a strength (E) and a direction.  The force felt by a charge in an electric field is F = qE.  E and F are in the same direction if q is positive (q > 0), opposite directions if q < 0.  Another way to say it: positive charges feel a force in the same direction as the field, negative charges in the opposite direction.  Unit of E is N/C.

Example Problem

Practice Problem  In a uniform electric field in empty space, a 4 C charge is placed and it feels an electrical force of 12 N. If this charge is removed and a 6 C charge is placed at that point instead, what force will it feel?

Practice Problem

Electric Potential  The potential energy due to a charge’s position in an electric field, PE = qV.  For gravity, we usually choose PE = 0 at the ground. For electricity, we usually choose PE = 0 at an infinite distance away.  Note: PE is usually measured in Joules, but we can also use electron volts (eV), the energy gained by the charge of 1 electron moving across 1 V.

Electric Potential  V is called “voltage” or “potential”, unit is J/C or volts (V).  V is the potential energy provided at each point in a field to a unit charge.  Usually potential difference is more important, as a measure of energy required to move a charged particle.  Also, it’s a scalar. Can you see why? (Hint: PE=qV)

Electric Potential  You increase the electric potential of an object or space by adding positive charge to it (or taking away negative charge from it).

Example Problem

Practice Problem

Example Problem

Equipotential Lines  Lines of equal potential, equal distance from point/surface of zero potential energy.  A charged particle can be moved along an equipotential line without work being done.  Always perpendicular to the electric field lines.

Equipotential Lines

Practice Problem  Draw the equipotential lines for two positive particles close to each other.

Which requires the most work, to move a positive charge from P to points 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 17.7aWork and Electric Potential I ConcepTest 17.7a Work and Electric Potential I

path #1 against hard to do For path #1, you have to push the positive charge against the E field, which is hard to do. By contrast, path #4 is the easiest, since the field does all the work. Which requires the most work, to move a positive charge from P to points 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 17.7aWork and Electric Potential I ConcepTest 17.7a Work and Electric Potential I

Which requires zero work, to move a positive charge from P to points 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 17.7bWork and Electric Potential II ConcepTest 17.7b Work and Electric Potential II

path #3 For path #3, you are moving in a direction perpendicular to the field lines. This means you are moving along an equipotential, which requires no work (by definition). Which requires zero work, to move a positive charge from P to points 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 17.7bWork and Electric Potential II ConcepTest 17.7b Work and Electric Potential II Follow-up: Which path requires the least work?

Parallel plates  Oppositely charged.  Useful because electric field between the is uniform in strength and direction (except at the edges).  E = V/d  Because qΔV=ΔPE=W=F·d=qE·d

Capacitor  Parallel plates added to a circuit.  Charge is added by a battery (movie).movie  Take out the battery, and charge flows back.  How much charge can a capacitor hold?  Q = CV (V is voltage of the battery)  How big is C?  C = ε 0 A/d  ε 0 is permittivity of free space, A is area of plates (m 2 ), d is separation of the plates (m).  Unit of C is Farads (F).

Practice Problem

Capacitor C 1 is connected across a battery of 5 V. An identical capacitor C 2 is connected across a battery of 10 V. Which one has the most charge? C 1 1) C 1 C 2 2) C 2 3) both have the same charge 4) it depends on other factors +Q+Q –Q–Q ConcepTest 17.8Capacitors ConcepTest 17.8 Capacitors

Q = C V greater voltagemost charge C 2 Since Q = C V and the two capacitors are identical, the one that is connected to the greater voltage has the most charge, which is C 2 in this case. Capacitor C 1 is connected across a battery of 5 V. An identical capacitor C 2 is connected across a battery of 10 V. Which one has the most charge? C 1 1) C 1 C 2 2) C 2 3) both have the same charge 4) it depends on other factors +Q+Q –Q–Q ConcepTest 17.8Capacitors ConcepTest 17.8 Capacitors

increase the area of the plates 1) increase the area of the plates decrease separation between the plates 2) decrease separation between the plates 3) decrease the area of the plates 4) either (1) or (2) 5) either (2) or (3) What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)? +Q –Q ConcepTest 17.9aVarying Capacitance I ConcepTest 17.9a Varying Capacitance I

Q = C V increase its capacitance increasing Adecreasing d Since Q = C V, in order to increase the charge that a capacitor can hold at constant voltage, one has to increase its capacitance. Since the capacitance is given by, that can be done by either increasing A or decreasing d. increase the area of the plates 1) increase the area of the plates decrease separation between the plates 2) decrease separation between the plates 3) decrease the area of the plates 4) either (1) or (2) 5) either (2) or (3) What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)? +Q –Q ConcepTest 17.9aVarying Capacitance I ConcepTest 17.9a Varying Capacitance I

A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled (without changing Q), what is the new value of the voltage? 100 V 1) 100 V 200 V 2) 200 V 3) 400 V 4) 800 V 5) 1600 V +Q+Q –Q–Q ConcepTest 17.9cVarying Capacitance III ConcepTest 17.9c Varying Capacitance III

Once the battery is disconnected, Q has to remain constant Q = C V voltage must double Once the battery is disconnected, Q has to remain constant, since no charge can flow either to or from the battery. Since when the spacing d is doubled, the capacitance C is halved. And since Q = C V, that means the voltage must double. A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled (without changing Q), what is the new value of the voltage? 100 V 1) 100 V 200 V 2) 200 V 3) 400 V 4) 800 V 5) 1600 V +Q+Q –Q–Q ConcepTest 17.9cVarying Capacitance III ConcepTest 17.9c Varying Capacitance III

Point charges  Electric field: E = kQ/r 2  Electric potential: V = kQ/r  Electric force: F = kQ 1 Q 2 /r 2  Electric field points away from positive charges, toward negative charges.  Electric potential is high, + near positive charges; low, - near negative charges.

Example Problem

Practice Problem

 Calculate the electric field and electric potential at point A.

Four point charges are arranged at the corners of a square. Find the electric field E and the potential V at the center of the square. 1) E = 0 V = 0 2) E = 0 V  0 3) E  0 V  0 4) E  0 V = 0 5) E = V regardless of the value -Q-Q-Q-Q -Q-Q-Q-Q +Q+Q+Q+Q +Q+Q+Q+Q ConcepTest 17.4Hollywood Square ConcepTest 17.4 Hollywood Square

Four point charges are arranged at the corners of a square. Find the electric field E and the potential V at the center of the square. 1) E = 0 V = 0 2) E = 0 V  0 3) E  0 V  0 4) E  0 V = 0 5) E = V regardless of the value -Q-Q-Q-Q -Q-Q-Q-Q +Q+Q+Q+Q +Q+Q+Q+Q potential is zero The potential is zero: the scalar contributions from the two positive charges cancel the two minus charges. it is non-zero However, the contributions from the electric field add up as vectors, and they do not cancel (so it is non-zero). ConcepTest 17.4Hollywood Square ConcepTest 17.4 Hollywood Square Follow-up: What is the direction of the electric field at the center?

At which point does V = 0? 1 3 2 4 +Q+Q–Q–Q 5) all of them ConcepTest 17.5aEquipotential Surfaces I ConcepTest 17.5a Equipotential Surfaces I

At which point does V = 0? 1 3 2 4 +Q+Q–Q–Q 5) all of them All of the points are equidistant from both charges cancel outeverywhere All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel out everywhere along the mid-plane between the charges. ConcepTest 17.5aEquipotential Surfaces I ConcepTest 17.5a Equipotential Surfaces I Follow-up: What is the direction of the electric field at all 4 points?

Which of these configurations gives V = 0 at all points on the x-axis? 4) all of the above 5) none of the above 1) x +2  C -2  C +1  C -1  C 2) x +2  C -1  C +1  C -2  C 3) x +2  C -1  C -2  C +1  C ConcepTest 17.5bEquipotential Surfaces II ConcepTest 17.5b Equipotential Surfaces II

Only in case (1), where opposite charges lie directly across the x-axis from each other, do the potentials from the two charges above the x-axis cancel the ones below the x-axis. Which of these configurations gives V = 0 at all points on the x-axis? 4) all of the above 5) none of the above 1) x +2  C -2  C +1  C -1  C 2) x +2  C -1  C +1  C -2  C 3) x +2  C -1  C -2  C +1  C ConcepTest 17.5bEquipotential Surfaces II ConcepTest 17.5b Equipotential Surfaces II

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