PhysicsII-week3-Capacitance and Current
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Electrostatics (静电学)
Chapter 19 Electric Charge and Electric Field Chapter 20 Gauss's Law Chapter 21 Electric Potential Chapter 22 Capacitance, Dielectrics, Electric Energy Storage
(b) Adding a battery imposes an electric potential difference between the ends of the loop that are connected to the terminals of the battery. The battery thus produces an electric field within the loop, from terminal to terminal, and the field causes charges to move around the loop. This movement of charges is a current i.
16
Current Density
17
Drift Speed
Current is said to be due to positive charges that are propelled by the electric field.
Let us assume that these charge carriers all move with the same drift speed vd and that the current density J is uniform across the wire’s cross-sectional area A. The number of charge carriers in a length L of the wire is nAL, where n is the number of carriers per unit volume. The total charge of the carriers in the length L, each with charge e, is then
Examples
Long line of charge. Determine the magnitude of the electric field at any point P a distance x from the midpoint 0 of a very long line (a wire, say) of uniformly distributed positive charge. Assume x is much smaller than the length of the wire, and let l be the charge per unit length (C/m).
where we have assumed the wire is extremely long in both directions
Applying Guass’s Law
For our chosen gaussian surface Gauss's law gives
where l is the length of our chosen gaussian surface (l << length of wire), and 2pR is its circumference.
vector form
q=(nAL)e
Because the carriers all move along the wire with speed vd, this total charge moves through any cross section of the wire in the time interval
Cylindrical Capacitor
A cylindrical capacitor consists of a cylinder (or wire) of radius Rb surrounded by a coaxial cylindrical shell of inner radius Ra (Ra-Rb << length of cylged (Q).
18
Homework
• HW3.1 A parallel-plate capacitor has fixed charges +Q and -Q. The separation of the plates is then tripled. (a) By what factor does the energy stored in the electric field change? (b) How much work must be done to increase the separation of the plates from d to 3.0d? The area of each plate is A. • HW3.2 In a dynamic random access memory (DRAM) computer chip, each memory cell chiefly consists of a capacitor for charge storage. Each of these cells represents a single binary-bit value of 1 when its 35-fF capacitor (1 fF = 10- 15 F) is charged at 1.5 V, or 0 when uncharged at 0 V. (a) When it is fully charged, how many excess electrons are on a cell capacitor's negative plate? (b) After charge has been placed on a cell capacitor's plate, it slowly "leaks" off (through a variety of mechanisms) at a constant rate of 0.30 fC/s. How long does it take for the potential difference across this capacitor to decrease by 1.0% from its fully charged value? (Because of this leakage effect, the charge on a DRAM capacitor is "refreshed" many times per second.)
DC Circuits
Chapter 23 Current and Resistance Chapter 24 Emf, Kirchhoff’s Rules, and RC circuits
12
Electric Current
(a) A loop of copper in electrostatic equilibrium. The entire loop is at a single potential, and the electric field is zero at all points inside the copper.
15
Question
The figure here shows a portion of a circuit. What are the magnitude and direction of the current i in the lower righthand wire?
? 8 A, rightward
Capacitance (电容)
• The capacitance C is defined as the ratio of Q to Vab. • The SI unit of capacitance is the farad (F): 1 F = 1 C/V. • A parallel-plate capacitor consists of two parallel conducting plates, each with area A, separated by a distance d. • If they are separated by vacuum, the capacitance depends only on A and d.
i0 = i1 + i2
A current arrow is drawn in the direction in which positive charge carriers would move, even if the actual charge carriers are negative and move in the opposite direction.
13
Electric Current
The current i through the conductor has the same value at planes aa’, bb’, and cc’.
1 ampere = 1 A =1 coulomb per second = 1 C/s.
14
Electric Current
Dielectrics (介质)
Induced Charge and Polarization (极化)
Parallel-plate capacitor, Dielectric between plates
Electric energy density in a dielectric
Gauss’s law in a dielectric
Capacitors (电容器)
Capacitors
• A capacitor is any pair of conductors separated by an insulating material. • When the capacitor is charged, there are charges of equal magnitude Q and opposite sign on the two conductors, and the potential Vab of the positively charged conductor with respect to the negatively charged conductor is proportional to Q.
Capacitors in Series (串联) and Parallel (并联)
Energy in a Capacitor
• The energy U required to charge a capacitor C to a potential difference V and a charge Q is equal to the energy stored in the capacitor. • This energy can be thought of as residing in the electric field between the conductors; the energy density (energy per unit volume) is proportional to the square of the electric-field magnitude.
Chapter 19 Electric Charge and Electric Field Chapter 20 Gauss's Law Chapter 21 Electric Potential Chapter 22 Capacitance, Dielectrics, Electric Energy Storage
(b) Adding a battery imposes an electric potential difference between the ends of the loop that are connected to the terminals of the battery. The battery thus produces an electric field within the loop, from terminal to terminal, and the field causes charges to move around the loop. This movement of charges is a current i.
16
Current Density
17
Drift Speed
Current is said to be due to positive charges that are propelled by the electric field.
Let us assume that these charge carriers all move with the same drift speed vd and that the current density J is uniform across the wire’s cross-sectional area A. The number of charge carriers in a length L of the wire is nAL, where n is the number of carriers per unit volume. The total charge of the carriers in the length L, each with charge e, is then
Examples
Long line of charge. Determine the magnitude of the electric field at any point P a distance x from the midpoint 0 of a very long line (a wire, say) of uniformly distributed positive charge. Assume x is much smaller than the length of the wire, and let l be the charge per unit length (C/m).
where we have assumed the wire is extremely long in both directions
Applying Guass’s Law
For our chosen gaussian surface Gauss's law gives
where l is the length of our chosen gaussian surface (l << length of wire), and 2pR is its circumference.
vector form
q=(nAL)e
Because the carriers all move along the wire with speed vd, this total charge moves through any cross section of the wire in the time interval
Cylindrical Capacitor
A cylindrical capacitor consists of a cylinder (or wire) of radius Rb surrounded by a coaxial cylindrical shell of inner radius Ra (Ra-Rb << length of cylged (Q).
18
Homework
• HW3.1 A parallel-plate capacitor has fixed charges +Q and -Q. The separation of the plates is then tripled. (a) By what factor does the energy stored in the electric field change? (b) How much work must be done to increase the separation of the plates from d to 3.0d? The area of each plate is A. • HW3.2 In a dynamic random access memory (DRAM) computer chip, each memory cell chiefly consists of a capacitor for charge storage. Each of these cells represents a single binary-bit value of 1 when its 35-fF capacitor (1 fF = 10- 15 F) is charged at 1.5 V, or 0 when uncharged at 0 V. (a) When it is fully charged, how many excess electrons are on a cell capacitor's negative plate? (b) After charge has been placed on a cell capacitor's plate, it slowly "leaks" off (through a variety of mechanisms) at a constant rate of 0.30 fC/s. How long does it take for the potential difference across this capacitor to decrease by 1.0% from its fully charged value? (Because of this leakage effect, the charge on a DRAM capacitor is "refreshed" many times per second.)
DC Circuits
Chapter 23 Current and Resistance Chapter 24 Emf, Kirchhoff’s Rules, and RC circuits
12
Electric Current
(a) A loop of copper in electrostatic equilibrium. The entire loop is at a single potential, and the electric field is zero at all points inside the copper.
15
Question
The figure here shows a portion of a circuit. What are the magnitude and direction of the current i in the lower righthand wire?
? 8 A, rightward
Capacitance (电容)
• The capacitance C is defined as the ratio of Q to Vab. • The SI unit of capacitance is the farad (F): 1 F = 1 C/V. • A parallel-plate capacitor consists of two parallel conducting plates, each with area A, separated by a distance d. • If they are separated by vacuum, the capacitance depends only on A and d.
i0 = i1 + i2
A current arrow is drawn in the direction in which positive charge carriers would move, even if the actual charge carriers are negative and move in the opposite direction.
13
Electric Current
The current i through the conductor has the same value at planes aa’, bb’, and cc’.
1 ampere = 1 A =1 coulomb per second = 1 C/s.
14
Electric Current
Dielectrics (介质)
Induced Charge and Polarization (极化)
Parallel-plate capacitor, Dielectric between plates
Electric energy density in a dielectric
Gauss’s law in a dielectric
Capacitors (电容器)
Capacitors
• A capacitor is any pair of conductors separated by an insulating material. • When the capacitor is charged, there are charges of equal magnitude Q and opposite sign on the two conductors, and the potential Vab of the positively charged conductor with respect to the negatively charged conductor is proportional to Q.
Capacitors in Series (串联) and Parallel (并联)
Energy in a Capacitor
• The energy U required to charge a capacitor C to a potential difference V and a charge Q is equal to the energy stored in the capacitor. • This energy can be thought of as residing in the electric field between the conductors; the energy density (energy per unit volume) is proportional to the square of the electric-field magnitude.