CK-12 People's Physics Book Version 2
Page 16
What is the power dissipated by the toasters?
Where would you put the fuses to make sure the toasters don't draw more than 15 Amps?
Where would you put a Amp fuse to prevent a fire (if too much current flows through the wires they will heat up and possibly cause a fire)?
Look at the following scheme of four identical light bulbs connected as shown. Answer the questions below giving a justification for your answer: Which of the four light bulbs is the brightest?
Which light bulbs are the dimmest?
Tell in the following cases which other light bulbs go out if:
bulb goes out (ii). bulb goes out (iii). bulb goes out
Tell in the following cases which other light bulbs get dimmer, and which get brighter if:
bulb goes out (ii). bulb goes out
Refer to the circuit diagram below and answer the following questions. What is the resistance between and ?
What is the resistance between and ?
What is the resistance between and ?
What is the the total equivalent resistance of the circuit?
What is the current leaving the battery?
What is the voltage drop across the resistor?
What is the voltage drop between and ?
What is the voltage drop between and ?
What is the current through the resistor?
What is the total energy dissipated in the if it is in use for 11 hours?
In the circuit shown here, the battery produces an emf of and has an internal resistance of . Find the total resistance of the external circuit.
Find the current drawn from the battery.
Determine the terminal voltage of the battery
Show the proper connection of an ammeter and a voltmeter that could measure voltage across and current through the resistor. What measurements would these instruments read?
Students measuring an unknown resistor take the following measurements:
Voltage Current
Show a circuit diagram with the connections to the power supply, ammeter and voltmeter.
Graph voltage vs. current; find the best-fit straight line.
Use this line to determine the resistance.
How confident can you be of the results?
Use the graph to determine the current if the voltage were .
Students are now measuring the terminal voltage of a battery hooked up to an external circuit. They change the external circuit four times and develop the following table of data:
Terminal Voltage Current
Graph this data, with the voltage on the vertical axis.
Use the graph to determine the emf of the battery.
Use the graph to determine the internal resistance of the battery.
What voltage would the battery read if it were not hooked up to an external circuit?
Students are using a variable power supply to quickly increase the voltage across a resistor. They measure the current and the time the power supply is on. The following table of data is developed:
Time(sec) Voltage Current
Graph voltage vs. current
Explain the probable cause of the anomalous data after seconds
Determine the likely value of the resistor and explain how you used the data to support this determination.
Graph power vs. time
Determine the total energy dissipation during the seconds.
You are given the following three devices and a power supply of exactly . Device is rated at and Device is rated at and Device is rated at and
Design a circuit that obeys the following rules: you may only use the power supply given, one sample of each device, and an extra, single resistor of any value (you choose). Also, each device must be run at their rated values.
Given three resistors, and and a power source connect them in a way to heat a container of water as rapidly as possible. Show the circuit diagram
How many joules of heat are developed after 5 minutes?
Construct a circuit using the following devices: a power source. Two resistors, device A rated at , ; device rated at , ; device rated at , ; device rated at , .
You have a battery with an emf of and an internal resistance of . Some are drawn from the external circuit. What is the terminal voltage
The external circuit consists of device , and ; device , and , and two resistors. Show how this circuit is connected.
Determine the value of the two resistors.
Students use a variable power supply an ammeter and three voltmeters to measure the voltage drops across three unknown resistors. The power supply is slowly cranked up and the following table of data is developed:
Current Voltage Voltage Voltage
Draw a circuit diagram, showing the ammeter and voltmeter connections.
Graph the above data with voltage on the vertical axis.
Use the slope of the best-fit straight line to determine the values of the three resistors.
Quantitatively discuss the confidence you have in the results
What experimental errors are most likely might have contributed to any inaccuracies.
Design a parallel plate capacitor with a capacitance of . You can select any area, plate separation, and dielectric substance that you wish.
You have a capacitor. How much voltage would you have to apply to charge the capacitor with of charge?
Once you have finished, how much potential energy are you storing here?
If all this energy could be harnessed to lift you up into the air, how high would you be lifted?
Show, by means of a sketch illustrating the charge distribution, that two identical parallel-plate capacitors wired in parallel act exactly the same as a single capacitor with twice the area.
A certain capacitor can store of charge if you apply a voltage of . How many volts would you have to apply to store of charge in the same capacitor?
Why is it harder to store more charge?
A certain capacitor can store of energy (by storing charge) if you apply a voltage of . How many volts would you have to apply to store of energy in the same capacitor? (Important: why isn’t the answer to this just ?)
Marciel, a bicycling physicist, wishes to harvest some of the energy he puts into turning the pedals of his bike and store this energy in a capacitor. Then, when he stops at a stop light, the charge from this capacitor can flow out and run his bicycle headlight. He is able to generate of electric potential, on average, by pedaling (and using magnetic induction). If Mars wants to provide A of current for 60 seconds at a stop light, how big a capacitor should he buy (i.e. how many farads)?
How big a resistor should he pass the current through so the RC time is three minutes?
Given a capacitor with between the plates a field of is established between the plates. What is the voltage across the capacitor?
If the charge on the plates is , what is the capacitance of the capacitor?
If two identical capacitors of this capacitance are connected in series what it the total capacitance?
Consider the capacitor connected in the following circuit at point with two switches and , a resistor and a power source:
i. Calculate the current through and the voltage across the resistor if is open and is closed ii. Repeat if is closed and is open
Figure for Problems 8-10:
Consider the figure above with switch, , initially open: What is the voltage drop across the resistor?
What current flows thru the resistor?
What is the voltage drop across the microfarad capacitor?
What is the charge on the capacitor?
How much energy is stored in that capacitor?
Find the capacitance of capacitors , , and if compared to the capacitor where...
(i). has twice the plate area and half the plate separation (ii). has twice the plate area and the same plate separation (iii). has three times the plate area and half the plate separation
Now the switch in the previous problem is closed. Wh
at is the total capacitance of branch II?
What is the total capacitance of branches I, II, and III taken together?
What is the voltage drop across capacitor ?
Reopen the switch in the previous problem and look at the capacitor. It has a plate separation of . What is the magnitude and direction of the electric field?
If an electron is released in the center to traverse the capacitor and given a speed the speed of light parallel to the plates , what is the magnitude of the force on that electron?
What would be its acceleration in the direction perpendicular to its motion?
If the plates are long, how much time would it take to traverse the plate?
What displacement toward the plates would the electron undergo?
With what angle with respect to the direction of motion does the electron leave the plate?
Design a circuit that uses capacitors, switches, voltage sources, and light bulbs that will allow the interior lights of your car to dim slowly once you get out.
Design a circuit that would allow you to determine the capacitance of an unknown capacitor.
The voltage source in the circuit below provides . The resistor is and the capacitor has a value of . What is the voltage across the capacitor after the circuit has been hooked up for a long time?
Answers to Selected Problems
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left = brighter, right = longer
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f. both resistors are brightest, then , then
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Chapter 16: Magnetism Version 2
The Big Idea
For static electric charges, the electromagnetic force is manifested by the Coulomb electric force alone. If charges are moving, an additional force emerges, called magnetism. The century realization that electricity and magnetism are dual aspects of the same force completely changed our understanding of the world we live in. As with electricity, we use a field formulation to keep track of magnetic forces. Magnetic fields are usually denoted by the letter and are measured in Teslas, in honor of the Serbian physicist Nikola Tesla; like electric fields, they are vector fields that contain energy, unlike electric fields, they have three dimensional properties and require some special vector rules to understand.
Insights due to Ampere, Gauss, and Maxwell led to the understanding that moving charges --- electric currents --- create magnetic fields. Varying magnetic fields create electric fields. Thus a loop of wire in a changing magnetic field will have current induced in it. This is called electromagnetic induction.
Sources of Magnetic Fields
In the electricity chapter, we learned that static electric fields have, as their source, some arrangement of charges. On the other hand, there are no sources of magnetic charge: every magnet, no matter how small, has a 'north' and 'south' pole. Nonetheless, there exist 'magnetic materials' that create fields and experience forces from other magnetic materials. In this chapter, we study magnetic fields produced by two different phenomena.
Permanent Magnets
Permanent magnets (like refrigerator magnets) consist of atoms, such as iron, for which the magnetic moments (roughly electron spin) of the electrons are “lined up” all across the atom. This means that their magnetic fields add up, rather than canceling each other out. The net effect is noticeable because so many atoms have lined up. The magnetic field of such a magnet always points from the north pole to the south. The magnetic field of a bar magnet, for example, is illustrated below:
If we were to cut the magnet above in half, it would still have north and south poles; the resulting magnetic field would be qualitatively the same as the one above (but weaker).
Charged Particles in Motion (Wires)
Charged particles in motion also generate magnetic fields. The most frequently used example is a current carrying wire, since current is literally moving charged particles. The magnitude of a field generated by a wire depends on distance to the wire and strength of the current : Meanwhile, its direction can be found using the so called first right hand rule: point your thumb in the direction of the current. Then, curl your fingers around the wire. The direction your fingers will point in the same direction as the field. Be sure to use your right hand!
Sometimes, it is necessary to represent such three dimensional fields on a two dimensional sheet of paper. The following example illustrates how this is done.
In the example above, a current is running along a wire towards the top of your page. The magnetic field is circling the wire in loops that are pierced through the center by the current. Where these loops intersect this piece of paper, we use the symbol to represent where the magnetic field is coming out of the page and the symbol to represent where the magnetic field is going into the page. This convention can be used for all vector quantities: fields, forces, velocities, etc.
Effects of Magnetic Fields
Force on a Charged Particle
As moving charges create magnetic fields, so they experience forces from magnetic fields generated by other materials. The magnitude of the force experienced by a particle traveling in a magnetic field depends on the charge of the particle , the velocity of the particle , the strength of the field , and, importantly, the angle between their relative directions : There is a second right hand rule that will show the direction of the force on a positive charge in a magnetic field: point your index finger along the direction of the particle’s velocity . If your middle finger points along the magnetic field, your thumb will point in the direction of the force. NOTE: For negative charge reverse the direction of the force (or use your left hand)
For instance, if a positively charged particle is moving to the right, and it enters a magnetic field pointing towards the top of your page, it feels a force going out of the page, while if a positively charged particle is moving to the left, and it enters a magnetic field pointing towards the top of your page, it feels a force going into the page:
Example 1: Find the Magnetic Field
Question: An electron is moving to the east at a speed of . It feels a force in the upward direction with a magnitude of . What is the magnitude and direction of the magnetic field this electron just passed through?
Answer: There are two parts to this question, the magnitude of the electric field and the direction. We will first focus on the magnitude.
To find the magnitude we will use the equation We were given the force of the magnetic field and the velocity that the electron is traveling . We also know the charge of the electron . Also, because the electron's velocity is perpendicular to the field, we do not have to deal with because of degrees is . Therefore all we have to do is solve for B and plug in the known values to get the answer. Now, plugging the known values we have Now we will find the direction of the field. We know the direction of the velocity (east) and the direction of the force due to the magnetic field (up, out of the page). Therefore we can use the second right hand rule (we will use the left hand, since an electron's charge is negative). Point the pointer finger to the right to represent the velocity and the thumb up to represent the force. This forces the middle finger, which represents the direction of the magnetic field, to point south. Alternatively, we could recognize that this situation is illustrated for a positive particle in the right half
of the drawing above; for a negative particle to experience the same force, the field has to point in the opposite direction: south.
Example 2: Circular Motion in Magnetic Fields
Consider the following problem: a positively charged particle with an initial velocity of , charge and mass traveling in the plane of this page enters a region with a constant magnetic field pointing into the page. We are interested in finding the trajectory of this particle.
Since the force on a charged particle in a magnetic field is always perpendicular to both its velocity vector and the field vector (check this using the second right hand rule above), a constant magnetic field will provide a centripetal force --- that is, a constant force that is always directed perpendicular to the direction of motion. Two such force/velocity combinations are illustrated above. According to our study of rotational motion, this implies that as long as the particle does not leave the region of the magnetic field, it will travel in a circle. To find the radius of the circle, we set the magnitude of the centripetal force equal to the magnitude of the magnetic force and solve for :