A



A.P. Physics Review Sheet 2

3/22/11

ELECTRICITY AND MAGNETISM

Electric Charge

• Charge is quantized with e = 1.60 x 10-19 C. Recall that you can use this as a conversion factor with units 1.60 x 10-19 C/electron, for example.

• Electrons have a negative charge, –e, protons have a positive charge, +e, and neutrons are electrically neutral.

• The SI unit of charge is the coulomb, C.

• Charge is conserved: The total charge in the universe is constant.

• Charge transfer occurs in two ways:

1. Charging through contact (ex. walking across a carpet, rubbing a balloon on your hair)

2. Charging by induction (recall electroscope demonstrations)

• Conductors, insulators, and semiconductors are compared in Table 1.

• A spherical distribution of charge, when viewed from the outside, behaves the same as an equivalent point charge at the center of the sphere.

• A van de Graaff generator collects electric charge (recall demonstrations)

| |

|Table 1: Conductors, Insulators, and Semiconductors |

|Material Type |Description |

| | |

|Conductor: |Each atom gives up one or more electrons that are then free to move throughout the material. |

| | |

|Insulator: |Does not allow electrons within it to move from atom to atom. |

| | |

|Semiconductor: |Has properties that are intermediate between those of insulators and conductors. |

Electric Force

• Electric charge, force, and field are compared in Table 2.

• Electric charges exert forces on one another along the line connecting them: Like charges repel, opposite charges attract.

• Compare and contrast electric force to gravitational force (Law of Universal Gravitation):

1. Both forces are field forces

2. Both are inverse square laws; recall that [pic] where G = 6.67 x 10-11 Nm2/kg2

3. Electric force is significantly stronger than gravitational force

4. Electric force can be attractive or repulsive whereas gravitational force is only attractive.

| |

|Table 2: Electric Charge, Force, and Field |

|Quantity |Value or Equation |Comments |

| | | |

|Electric Charge: |e = 1.60 x 10-19 C |Charge comes in quantized amounts that are |

| | |always integer multiples of e. |

| |Charge on an electron is –e. | |

| |Charge on a proton is +e. | |

| | | |

|Electric Force: |[pic] and |Electric force is a |

| | |conservative force. |

| |[pic] where | |

|(The lower equation is called Coulombs’s Law): | |Superposition principle is followed: the |

| |[pic]8.99 x 109 Nm2/C2 |electric force on one charge due to two or more|

| | |other charges is the vector sum of each |

| | |individual force. |

| | | |

|Electric Field: |[pic] and |1 N/C = 1 V/m |

| | | |

| |[pic] |Superposition principle is followed: the total|

| | |electric field due to two or more charges is |

| |[pic] (or [pic]) |given by the vector sum of the fields due to |

| | |each charge individually. |

Electric Field

• The electric field is the force per charge at a given location in space.

• The electric field vector, [pic], points in the direction experienced by a positive test charge.

• Electric field strength depends on charge and distance

• Electric fields can be represented by electric field lines. Rules for drawing electric field lines are given in Table 3.

| |

|Table 3: Rules for Drawing Electric Field Lines |

|Number |Rule |

| | |

|Rule 1: |Electric field lines point in the direction of the electric field vector, [pic], at all times. |

| | |

|Rule 2: |Electric field lines start at positive charges or at infinity. |

| | |

|Rule 3: |Electric field lines end at negative charges or at infinity. |

| | |

|Rule 4: |Electric field lines are more dense the greater the magnitude of [pic]. In other words, for a |

| |set of point charges, the number of electric field lines connected to each charge is |

| |proportional to the magnitude of the charge. |

| | |

|Rule 5: |The electric field is always perpendicular to the equipotential surfaces, and it points in the |

| |direction of decreasing (more negative) electric potential (voltage). |

| | |

|Rule 6: |The electric field is perpendicular to the surface of a conductor. |

Shielding and Charging by Induction

• Excess charge on a conductor, zero field within a conductor, shielding, and charging by induction are compared in Table 4.

• Connecting a conductor to the ground is referred to as grounding. The ground itself is a good conductor, and it can give up or receive an unlimited number of electrons.

• Charge tends to accumulate at sharp points on a conductor’s surface.

| |

|Table 4: Shielding and Charging by Induction |

|Concept |Description |

| | |

|Excess Charge on a |Excess charge placed on a conductor, whether positive or negative, moves to the exterior |

|Conductor: |surface of the conductor. |

| | |

|Zero Field within a |The electric field within a conductor in equilibrium is zero. Thus, a conductor shields a |

|Conductor (Shielding): |cavity within it from external electrical fields. |

| | |

|Charging by Induction: |A conductor can be charged without direct physical contact with another charged object. This |

| |is charging by induction. |

Electric Potential Energy

• The electric force is conservative, just like the force of gravity. As a result, there is a potential energy [pic] associated with the electric force.

• Electric potential energy shares many similarities with gravitational potential energy. For example, [pic] changes only in the direction parallel to the field whereas [pic] for movement perpendicular to the field. (Recall that gravitational potential energy is zero when an object moves sideways maintaining the same height off of the ground. The same is true for a test charge that moves perpendicular to an electric field.)

• Electric potential energy and gravitational potential energy are compared in Table 5.

• The change in electric potential energy is defined by [pic], where [pic] is the work done by the electric field.

| |

|Table 5: Electric Potential Energy and Gravitational Potential Energy |

| | | |

| |Electric Potential Energy ([pic]) |Gravitational Potential Energy ([pic]) |

|Movement | | |

| | | |

|Charge or object moves a small distance |[pic] is small |[pic] is small |

|against the field: | | |

| | | |

|Charge or object moves a large distance |[pic] is large |[pic] is large |

|against the field: | | |

| | | |

|Charge or object maintains a constant distance|[pic] |[pic] |

|as it moves perpendicular to the field: | | |

Electric Potential = Potential Difference = Voltage

• The change in electric potential is defined by [pic].

• The electric field is related to the rate of change of the electric potential. In particular, if the electric potential changes by the amount [pic] with a displacement [pic], the electric field in the direction of the displacement is [pic].

• Electric potential energy and electric potential (voltage) are compared in Table 6.

• Electric potential energy and electric potential (voltage) for point charges are compared in Table 7.

• For point charges, the electric potential forms a “potential hill” near a positive charge and a “potential well” near a negative charge. See Fig. 20-5 (p.670) for related diagrams.

| |

|Table 6: Electric Potential Energy and Electric Potential |

| | |Electric Potential (V) |

| | |(Also called Potential Difference or Voltage) |

|Condition |Electric Potential Energy (U) | |

| | | |

|Test charge moves against the electric field: |[pic] |[pic] |

| | | |

|Test charge moves in the same direction as the|[pic] |[pic] |

|electric field: | | |

| | | |

|Test charge moves perpendicular to the |[pic] |[pic] since |

|electric field: | | |

| | |[pic] |

| |

|Table 7: Electric Potential Energy and Electric Potential for Point Charges |

|Quantity |Equation |Comments |

| | | |

|Electric Potential Energy |[pic] |[pic] when the separation between the point |

|for Point Charges: | |charges [pic] and [pic] is infinite. |

| |[pic] | |

| | |Superposition principle is followed: the total|

| |[pic]8.99 x 109 Nm2/C2 |electric potential energy of two or more point |

| | |charges is the sum of the potential energies |

| | |due to each pair of charges. |

| | | |

|Electric Potential (Voltage) |[pic] |[pic] at an infinite distance from the point |

|for Point Charges: | |charge. |

| | | |

| | |Superposition principle is followed: the total|

| | |electric potential of two or more point charges|

| | |is the sum of the potentials due to each |

| | |separate charge. |

Energy Conservation

• Since electric force is a conservative force, electric potential energies can be calculated, and conservation of energy calculations can be performed.

• As usual, energy conservation can be expressed as [pic] where equations for the appropriate kinetic and potential energies appear in Table 8.

• Positive charges accelerate in the direction of decreasing electric potential; negative charges accelerate in the direction of increasing electric potential.

| |

|Table 8: Energy Conservation Calculations |

|Energy Type |Equation |Comments |

| | | |

|Kinetic Energy: |[pic] |The moving particle is usually a proton, |

| | |electron, or point charge. |

| | | |

|Electric Potential Energy: |[pic] |(1) When particles are accelerated through a |

| | |potential difference, [pic] is used. |

| | | |

| |[pic] |(2) When point charges are involved, [pic] is |

| | |used. |

| |[pic]8.99 x 109 Nm2/C2 | |

Work

• Table 9 shows how to calculate the work involved in moving charges within an electric field.

| |

|Table 9: Work Calculations |

|Type of Work |Equation |Comments |

| | | |

|Work done BY an electric |[pic] |This comes from the definition for a change in |

|field: | |electric potential energy. |

| | | |

|Work you do to move a |[pic] |Recall that [pic] when charges are moved to |

|charge AGAINST the field: | |infinity. To calculate [pic], sum the electric|

| | |potential energies due to other charges within |

| | |the system. |

Capacitors

• A capacitor is a device that stores electric charge and electrical energy.

• A parallel-plate capacitor consists of two oppositely charged, conducting parallel plates separated by a finite distance. The electric field is perpendicular to the plates, and it is uniform in magnitude and direction.

• Table 10 compares the definition of capacitance, the capacitance of a parallel-plate capacitor, the capacitance of a parallel-plate capacitor filled with a dielectric, and the electrical energy stored in a capacitor.

| |

|Table 10: Capacitance and Capacitors |

|Quantity |Equation |Comments |

| | | |

|Capacitance Definition: |[pic] |Capacitance is defined as the amount of charge,|

| | |[pic], stored in a capacitor per volt of |

| | |potential difference, [pic], between the |

| | |plates. |

| | | |

|Capacitance of a Parallel- |[pic] where |[pic] is the “permittivity of free space.” |

|plate Capacitor: |[pic] 8.85 x 10-12 C2/Nm2 | |

| | | |

|Capacitance of a Parallel- |[pic] where |For us, a dielectric is an insulating material |

|plate Capacitor filled with |[pic] dielectric constant from |that increases the capacitance of a capacitor. |

|a Dielectric: |Table 20-1. | |

| | | |

|Electrical Energy Stored in |[pic] |In addition to storing charge, a capacitor also|

|a Capacitor: | |stores electrical energy. |

Electric Current

• Current is the rate of charge movement [pic] where [pic] is current in Amps (A), [pic] is charge passing through a given area in Coulombs (C), and [pic] is change in time in seconds (s). By definition, 1 Amp is one Coulomb per second (1 A = 1 C/s).

• By definition, the direction of the current [pic] in a circuit is the direction in which positive charges would move. The actual charge carriers, however, are generally electrons, which move opposite in direction to [pic].

• Drift velocity—net velocity of charge carriers (drift speed is relatively small; 68 min. on average for an electron to travel 1.0 m)

• Current sources

1. Batteries—change chemical energy into electrical energy

2. Generators—change mechanical energy into electrical energy

• There are two types of current: Direct current (DC) and alternating current (AC).

Resistance

• When electrons move through a wire, they encounter resistance to their motion. In order to move electrons against this resistance, it is necessary to apply a potential difference (voltage) between the ends of the wire.

• Ohm’s Law is [pic] where [pic] is potential difference (voltage) in Volts (V), [pic] is current in Amps (A), and [pic] is resistance in Ohms (Ω).

• See Table 11 for a comparison of the electrical quantities in Ohm’s Law and their water analogies.

• Ohmic versus nonohmic materials:

1. Ohmic materials have a constant resistance over a wide range of potential differences (ex. most metals)

2. Nonohmic materials do not have a constant resistance over a wide range of potential differences. (ex. diodes, which are analogous to check valves in plumbing)

• For an ohmic material, Ohm’s Law can be experimentally determined by plotting the current (x-axis) against the voltage (y-axis). The equation for the resulting line is [pic] where the slope is the resistance, [pic], and the y-intercept is 0 since the line passes through the origin.

• Factors affecting resistance include length of conductor, cross-sectional area of a conductor, conductor material, and temperature.

• [pic] where [pic] is resistance in Ohms, [pic] is potential difference (voltage) in Volts, [pic] is current in Amps, [pic] is resistivity in Ohm-meters (See Table 21-1 on p.700), [pic] is the length of the conductor in meters, and [pic] is the conductor’s cross-sectional area in m2.

• Resistors can be used to control the amount of current in a conductor. As resistance increases, current decreases at constant voltage.

• Superconductors have no resistance below a critical temperature.

• Salt water and perspiration lower the body’s resistance.

| |

|Table 11: Electrical Quantities in Ohm’s Law and Their Water Analogies |

|Electrical Quantity |Description |Unit |Water Analogy |

| | | | |

|Electric Potential (Voltage) |Energy difference per unit charge |Volt (V) |Water Pressure |

| |between two points in a circuit. | | |

| | | | |

|Current |Amount of charge flowing per unit |Ampere (A) |Amount of water flowing per unit |

| |time. | |time. |

| | | | |

|Resistance |A measure of how difficult it is |Ohm (() |A measure of how difficult it is |

| |for electrical current to flow in a| |for water to flow through a pipe. |

| |circuit. | | |

Electric Power

• Electric power, [pic], is the rate at which electrical energy is converted to other forms of energy. It can be calculated using [pic] where [pic] is power in Watts (W), [pic] is current in Amps (A), and [pic] is potential difference (voltage) in Volts (V).

• [pic] and [pic] are both combinations of the power formula, [pic], and Ohm’s Law, [pic].

• Most light bulbs are labeled with their electric power rating in Watts; the amount of heat and light given off by the bulb is related to the power rating.

• Electric companies measure energy consumed in kilowatt hours (1 kWh = 3.6 x 106 J)

• Electrical energy is transferred at high potential differences (voltages) to minimize energy loss.

Schematic Diagrams

• Make sure you can read, understand, and draw schematic diagrams.

• Know the symbols for wire, resistor, battery, open and closed switch, capacitor, bulb, and plug.

• Be able to identify open circuits, closed circuits, and short circuits

• Short circuits occur when there is little or no resistance to the movement of charges; the increase in current may cause the wire to overheat and start a fire.

• When a light bulb is screwed in, charges can enter through the base, move along the wire to the filament, and exit the bulb through the threads.

• Light bulbs emit light because the filament is a resistor which converts some electrical energy to light energy and heat energy.

• The electromotive force (emf) is the source of a circuit’s potential difference (voltage) and electrical energy.

Resistors in Series and Parallel Circuits

• Be able to use Ohm’s Law, [pic], and the information in Table 12 to determine the equivalent resistance, [pic], current, [pic], and voltage [pic], for complex circuits containing both series and parallel parts.

• For complex circuits containing batteries, Ohm’s Law, [pic], is expressed as [pic] where [pic] is the battery’s emf (voltage), [pic] is the current passing through the battery, and [pic] is the circuit’s equivalent resistance.

• In real life, batteries have a small internal resistance that must be included in calculations when current is flowing. However, when current is not flowing like when a circuit switch is open, this internal resistance is ignored.

• Kirchoff’s rules in Table 13 are statements of charge conservation and energy conservation as applied to closed electrical circuits. Kirchoff’s rules give an alternate way to find current and voltage in complex circuits.

| |

|Table 12: Series and Parallel Circuits |

|Quantity |Series Circuit |Parallel Circuit |

| | | |

|Equivalent Resistance, [pic]: |[pic] |[pic] |

| | | |

|Current, [pic]: |[pic] |[pic] |

| | | |

|Voltage, [pic]: |[pic] |[pic] |

|(emf, [pic], when batteries are involved) | | |

| |

|Table 13: Kirchhoff’s Rules |

|Rule |Description |

| | |

|Junction Rule: |The algebraic sum of all currents meeting at a junction must equal zero. Currents entering the|

|(Charge Conservation) |junction are taken to be positive; currents leaving the junction are taken to be negative. |

| | |

|Loop Rule: |The algebraic sum of all potential differences around a closed loop is zero. The potential |

|(Energy Conservation) |increases in going from the negative to the positive terminal of a battery and decreases when |

| |crossing a resistor in the direction of the current. |

Capacitors in Series and Parallel Circuits

• For complex circuits containing multiple capacitors, capacitance, [pic], is expressed as [pic] where [pic] is the battery’s emf (voltage), [pic] is the circuit’s total charge, and [pic] is the circuit’s equivalent capacitance.

• See Table 14 to determine equivalent capacitance, charge, and voltage for capacitors in series and parallel circuits.

| |

|Table 14: Capacitors in Series and Parallel Circuits |

|Quantity |Series Circuit |Parallel Circuit |

| | | |

|Equivalent Capacitance, |[pic] |[pic] |

|[pic]: | | |

| | | |

|Charge, [pic]: |[pic] |[pic] |

| | | |

|Voltage, [pic]: |[pic] |[pic] |

|(emf, [pic], when batteries are involved) | | |

Resistor-Capacitor (RC) Circuits

• In circuits containing both resistors and capacitors, there is a characteristic time, [pic], during which significant changes occur. This time is referred to as the time constant. The simplest such circuit, known as an [pic] circuit, consists of one resistor and one capacitor connected in series.

• Table 15 gives equations describing the charge, electric potential (voltage), and current for a capacitor in an [pic] circuit that is charging and discharging.

Ammeters, Voltmeters, and Multimeters

• Ammeters and voltmeters are devices for measuring currents and voltages, respectively, in electrical circuits.

• Ammeters, voltmeters, and multimeters are compared in Table 16.

| |

|Table 15: RC Circuit (One Resistor and One Capacitor Connected in Series) |

|The Capacitor is: |Quantity |Equation |

| | | |

|Charging: |Charge, [pic]: |[pic] |

| | |where [pic] time constant |

| | | |

|Charging: |Potential, [pic]: |[pic] |

| | | |

|Charging: |Current, [pic]: |[pic] |

| | | |

|Discharging: |Charge, [pic]: |[pic] where |

| | |[pic] time constant and the circuit starts with |

| | |charge [pic] at time [pic]. |

| | | |

|Discharging: |Potential, [pic]: |[pic] |

| |

|Table 16: Ammeters, Voltmeters, and Multimeters |

|Meter Type |Connected in: |Ideal Case |Comments |

| | | | |

|Ammeter: |Series |Resistance is zero |Measures electric |

| | | |current in Amps |

| | | | |

|Voltmeter: |Parallel |Resistance is infinite |Measures electric |

| | | |potential in Volts |

| | |

|Multimeter: |Measures electric current in Amps, electric potential in Volts, and resistance in Ohms depending on the |

| |instrument settings. |

Magnetic Field

• A magnet is characterized by two poles, referred to as the north pole and the south pole. All magnets have both poles. Like poles repel and unlike poles attract.

• Magnetic fields can be represented with lines similar to the way electric fields can be portrayed. In particular, the more closely spaced the lines, the more intense the magnetic field.

• Magnetic field lines, which point away from north poles and toward south poles, always form closed loops.

• The magnetic field of a bar magnet can be traced with a compass. The magnetic field lines are drawn so that they point from the north magnetic pole to the south magnetic pole in the direction the compass indicates.

• The Earth produces its own magnetic field. The geographic north pole of the Earth is actually the south magnetic pole of the Earth’s magnetic field.

• Soft magnetic materials like iron are easily magnetized but tend to lose their magnetism easily. For example, heating, cooling, or hammering iron promotes loss of magnetism.

• Hard magnetic materials like cobalt and nickel are difficulty magnetized, but once they are magnetized, they tend to retain their magnetism.

Magnetic Force

• Table 17 compares magnetic force with electric force.

• In order for a magnetic field to exert a force on a particle, the particle must have charge and it must be moving.

• The magnitude of the magnetic force is [pic] where [pic] is in Newtons (N), [pic] is the magnitude of the charge in Coulombs (C), [pic] is the speed of the charge in m/s, [pic] is the strength of the magnetic field in Tesla (T), and [pic] is the angle between the velocity vector [pic] and the magnetic field vector [pic].

• Table 18 gives the magnetic force right-hand rule and contrasts it with the magnetic field right-hand rule.

• Recall that for protons [pic] = +1.60 x 10-19 C, and for electrons [pic] = -1.60 x 10-19 C.

• An electric current in a wire is caused by the movement of electric charges. Since moving electric charges experience magnetic forces, it follows that a current-carrying wire will as well.

• See Table 19 to compare the magnetic force on moving charges, the magnetic force exerted on a current-carrying wire, and the magnetic forces between current-carrying wires.

• Wires that carry current in the same direction attract each other, and wires with oppositely directed currents repel each other.

| |

|Table 17: Comparison of Magnetic Force and Electric Force |

|Dependence |Magnetic Force |Electric Force |

| | | |

|Depends on the charge of the |Yes |Yes |

|particle, [pic]: | | |

| | | |

|Depends on the magnitude of |Yes, it depends on the [pic] field |Yes, it depends on the [pic] field |

|the corresponding field: | | |

| | | |

|Depends on the speed of the |Yes, which means that if [pic], then [pic]. |No, static charged particles have electric |

|particle, [pic]: |The particle must be moving to have a magnetic |forces. |

| |force. | |

| | | |

|Depends on the angle, [pic], |Yes |No |

|between the velocity vector, | | |

|[pic], and the corresponding | | |

|field vector, [pic] or [pic]: | | |

| | | |

|Corresponding Equation: |[pic] |[pic] |

| |where [pic] is perpendi- | |

| |cular to both [pic] and [pic] | |

| |

|Table 18: Right-Hand Rules for Magnetism |

|Rule Name |Rule |

| | |

|Magnetic Force Right-Hand |The magnetic force, [pic], points in a direction that is perpendicular to both [pic] and [pic].|

|Rule: |For a positive charge, point the fingers of your right hand in the direction of [pic] and curl |

| |them toward the direction of [pic]. Your thumb points in the direction of the magnetic force, |

| |[pic]. The force on a negative charge is in the opposite direction to that on a positive |

| |charge. |

| | |

|Magnetic Field Right-Hand |The direction of the magnetic field produced by a current is found by pointing the thumb of the|

|Rule: |right hand in the direction of the current. The fingers of the right hand curl in the |

| |direction of the field. |

| |

|Table 19: Comparison of Magnetic Forces |

|Magnetic Force Type |Equation |Comments |

| | | |

|Magnetic Force on Moving |[pic] |(1) Particle must have a charge and be moving |

|Charges: | |to have a magnetic force. |

| | |(2) [pic] is perpendicular to both [pic] and |

| | |[pic]; see magnetic force right-hand rule. |

| | | |

|Magnetic Force Exerted on a |[pic] where |[pic] is perpendicular to both [pic] and [pic];|

|Current-Carrying Wire: |[pic] wire length |see magnetic force right-hand rule. |

| | | |

|Magnetic Forces between |[pic] where |Wires that carry current in the same direction |

|Current-Carrying Wires: |[pic] 4π x 10-7 Tm/A and |attract one another; wires that carry current |

| |[pic] distance between wires |in opposite directions repel one another. |

Motion of Charged Particles in a Magnetic Field

• Table 20 compares the motion of a charged particle in an electric and a magnetic field.

• Table 21 compares constant-velocity straight-line motion, circular motion, and helical motion for charged particles in a magnetic field.

• If a charged particle moves perpendicular to a magnetic field, it will orbit with a constant speed in a circle of radius [pic] with [pic] where [pic] is in meters (m), [pic] is the mass of the charge in kg, [pic] is the speed of the charge in m/s, [pic] is the magnitude of the charge in Coulombs (C), and [pic] is the strength of the magnetic field in Tesla (T),

Electric Currents, Magnetic Fields, and Ampere’s Law

• The key observation that serves to unify electricity and magnetism is that electric currents cause magnetic fields. Hans Christian Oersted first discovered this in 1820 when he observed that a compass needle deflected when electrical current flowed through a wire.

• Table 18 gives the magnetic field right-hand rule and contrasts it with the magnetic force right-hand rule.

• Ampere’s Law

• Table 22 compares the magnetic field of a long straight wire, the magnetic field at the center of a current loop, and the magnetic field of a solenoid.

| |

|Table 20: Motion of a Charged Particle in an Electric Field and a Magnetic Field |

|Quantity Compared |Electric Field |Magnetic Field |

| | | |

|Motion of a charged particle: |A charged particle in an electric field, [pic],|A charged particle in a magnetic field, [pic], |

| |accelerates in the direction of the field. |accelerates perpendicular to both the direction|

| | |of the field and the velocity, [pic]. |

| | | |

|Speed of the particle: |Speed changes; a charged particle accelerates |Speed is constant; a charged particle |

| |in the direction of an electric field, [pic]. |accelerates perpendi-cular to both the |

| | |direction of a magnetic field, [pic], and the |

| | |velocity, [pic]. Thus, the particle changes |

| | |direction rather than velocity, which leads to |

| | |circu-lar motion at constant speed. |

| | | |

|Work done on the particle: |An electric field, [pic], can do work on a |A constant magnetic field, [pic], cannot do |

| |charged particle. |work on a charged particle because the magnetic|

| | |force is always perpendicular to the velocity, |

| | |[pic]. |

| |

|Table 21: Motion of Charged Particles in a Magnetic Field |

|Motion Type for Particle |Description |

| | |

|Constant Velocity, Straight-Line Motion: |If a charged particle moves parallel or antiparallel to a magnetic field, it experiences no |

| |magnetic force since [pic]. Thus, its velocity remains constant. |

| | |

|Circular Motion: |If a charged particle moves perpendicular to a magnetic field, it will orbit with a constant |

| |speed in a circle of radius [pic]: |

| |[pic] |

| | |

|Helical Motion: |When a particle’s velocity has components both parallel and perpendicular to a magnetic field, |

| |it will follow a helical path. (Recall the double helix of DNA to remember what a helical path|

| |means.) |

Electromagnetism and Magnetic Domains

• Use the second of our right-hand rules to determine the direction of a magnetic field around a current-carrying wire. If the thumb of your right hand points in the direction of the current, the fingers point in the direction of the magnetic field, B, around the wire.

• This right-hand rule can also be applied to a current-carrying loop to find the direction of the magnetic field.

• A solenoid produces a strong magnetic field by combining several current-carrying loops. A solenoid is helically wound coil of wire shaped like a Slinky.

| |

|Table 22: Comparison of Magnetic Fields |

|Magnetic Field Type |Equation |Comments |

| | | |

|Magnetic Field of a Long, |[pic] where |[pic] permeability of free space, which has |

|Straight Wire: |[pic] 4π x 10-7 Tm/A |values of: |

| |[pic] radial distance from wire |[pic] 4π x 10-7 Tm/A or |

| | |[pic] 1.26 x 10-6 Tm/A |

| | | |

|Magnetic Field at the Center |[pic] |A single loop of current produces a magnetic |

|of a Current Loop: |[pic] number of loops |field much like that of a permanent magnet. |

| |[pic] radius of loops | |

| | | |

|Magnetic Field of a Solenoid: |[pic] |The magnetic field inside a solenoid is nearly |

| |[pic] number of loops |uniform and aligned along the solenoid’s axis. |

| |[pic] length of solenoid |The magnetic field outside a solenoid is small,|

| |[pic] number of loops per length; [pic]. |and in the ideal case can be considered to be |

| | |zero. |

Induced Current

• Electromagnetic induction means inducing a current with a changing magnetic field.

• Be able to explain the significance of electromagnetic induction in modern society.

• Methods for inducing an electromotive force (emf) in a current loop:

1. Moving the loop into or out of the magnetic field.

2. Rotating the loop within the magnetic field.

3. Changing the strength of the magnetic field through the static loop.

4. Altering the loop’s shape.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download