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essential university physics

Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions

You’re designing a prosthetic ankle that includes a miniature electric motor containing a 150-turn circular coil 15 mm in diameter. The motor needs to develop a maximum torque of 3.1 mNm. The strongest magnets available that will fit in the prosthesis produce a 220-mT field. What current do you
An electron is moving in a uniform 0.25-T magnetic field; its velocity components parallel and perpendicular to the field are both 3.1 Mm/s.(a) What’s the radius of the electron’s spiral path?(b) How far does it move along the field direction in the time it takes to complete a full orbit about
90-cm-diameter cyclotron with a 2.0-T magnetic field is used to accelerate deuterium nuclei (one proton plus one neutron).(a) At what frequency should the dee voltage be alternated?(b) What’s the maximum kinetic energy of the deuterons?(c) If the magnitude of the potential difference between the
Show that the orbital radius of a charged particle moving at right angles to a magnetic field B can be written r = √12Km/qB, where K is the kinetic energy in joules, m the particle’s mass, and q its charge.
A beam of electrons moving in the x-direction at 8.7 Mm/s enters a region where a uniform 180-G magnetic field points in the y-direction. The boundary of the field region is perpendicular to the beam. How far into the field region does the beam penetrate?
A simplified model of Earth’s magnetic field has it originating in a single current loop at the outer edge of the planet’s liquid core (radius 3000 km). What current would give the 62μT field measured at the north magnetic pole?
A proton moving with velocity v1(vector) = 3.6x104ĵ m/s experiences a magnetic force of 7.4x10-16î N. A second proton moving on the x-axis experiences a magnetic force of 2.8x10-16ĵ N. Find the magnitude and direction of the magnetic field (assumed uniform), and the velocity of the second
Jupiter has the strongest magnetic field in our solar system, about 14 G at its poles. Approximating the field as that of a dipole, find Jupiter’s magnetic dipole moment.
A particle carrying a 50μC charge moves with velocity v(vector) = 5.0î + 3.2k̂ m/s through a magnetic field given by B(vector)= 9.4 î + 6.7 ĵ T.(a) Find the magnetic force on the particle.(b) Form the dot products F(vector)•V(vector) and F(vector)•B(vector) to show explicitly that
A superconducting solenoid has 3300 turns per meter and carries 4.1 kA. Find the magnetic field strength in the solenoid.
Number 12 gauge wire, commonly used in household wiring, is 2.053 mm in diameter and can safely carry currents of up to 20.0 A. For a wire carrying this maximum current, find the magnetic field strength(a) 0.150 mm from the wire’s axis,(b) at the wire’s surface, and (c) 0.375 mm beyond the
The line integral of the magnetic field on a closed path surrounding a wire has the value of 8.8 μTm. Find the current in the wire.
An electric motor contains a 250-turn circular coil 6.2 cm in diameter. If it develops a maximum torque of 1.2 Nm at a current of 3.3 A, what’s the magnetic field strength?
A single-turn square wire loop 18.0 cm on a side carries a 1.25-A current.(a) What’s the loop’s magnetic dipole moment?(b) What’s the magnitude of the torque the loop experiences when it’s in a 2.12-T magnetic field with the loop’s dipole moment vector at 65.0° to the microwaves?
Earth’s magnetic dipole moment is 8.0x1022 Am2 . Find the magnetic field strength at Earth’s magnetic poles.
What’s the current in a long wire if the magnetic field strength 1.2 cm from the wire’s axis is 67 μT?
A 2.2-m-long wire carrying 3.5 A is wound into a tight coil 5.0 cm in diameter. Find the magnetic field at its center.
A single-turn wire loop is 2.0 cm in diameter and carries a 650-mA current. Find the magnetic field strength(a) at the loop center and(b) on the loop axis, 20 cm from the center.
A wire carries 6.71 A. You form it into a single-turn circular loop and measure a magnetic field of 42.8 μT at the loop center.(a) What’s the loop’s radius?(b) What’s the field strength on the loop axis at 10.0 cm from the loop center?
A wire with mass per unit length 75 g/m runs horizontally at right angles to a horizontal magnetic field. A 6.2-A current in the wire results in its microwaves against gravity. What’s the magnetic field strength?
You’re on a team performing a high-magnetic-field experiment. A conducting bar carrying 4.1 kA will pass through a 1.3-m-long region containing a 12-T magnetic field, making a 60° angle with the microwaves. A colleague proposes resting the bar on wooden blocks. You argue that it will have to be
A wire carrying 15 A makes a 25° angle with a uniform magnetic field. The magnetic force per unit length of wire is 0.31 N/m. Find(a) the magnetic field strength and(b) the maximum force per unit length that could be achieved by reorienting the wire.
Find the magnitude of the force on a 65.5-cm-long wire carrying 12.0 A at right angles to a 475-G magnetic field.
Two protons, moving in a plane perpendicular to a uniform 500-G magnetic field, undergo an elastic head-on collision. How much time elapses before they collide again?
In a microwave oven, electrons describe circular motion in a magnetic field within a special tube called a magnetron; the electrons’ motion results in the production of microwaves.(a) If the electrons circle at a frequency of 2.45 GHz, what’s the magnetic field strength?(b) If the magnetron can
Radio astronomers detect electromagnetic radiation at a frequency of 42 MHz from an interstellar gas cloud. If the radiation results from electrons spiraling in a magnetic field, what’s the field strength?
How long does it take an electron to complete a circular orbit perpendicular to a 1.0-G magnetic field?
Find the radius of the path described by a proton moving at 15 km/s in a plane perpendicular to a 400-G magnetic field.
A velocity selector uses a 60-mT magnetic field perpendicular to a 24-kN/C electric field. At what speed will charged particles pass through the selector undeflected?
The magnitude of Earth’s magnetic field is about 0.5 gauss near Earth’s surface. What’s the maximum possible magnetic force on an electron with kinetic energy of 1 keV? Compare with the gravitational force on the electron.
Find the magnitude of the magnetic force on a proton moving at 2.5x105 m/s(a) perpendicular;(b) at 30°;(c) parallel to a 0.50-T magnetic field.
An electron moving at right angles to 0.10-T magnetic field experiences an acceleration of 6.0x1015 m/s2.(a) What’s its speed?(b) By how much does its speed change in 1 ns?
Find (a) the minimum magnetic field needed to exert a 5.4-fN force on an electron moving at 21 Mm/s (b) the field strength required if the field were at 45° to the electron’s velocity.
You’re about to purchase a battery. Normally, batteries are rated in ampere-hours—the total charge they can deliver. Your application calls for a 5Ah battery. But the 6-V battery you see while shopping online is rated at 50 watt-hours. Will it work?
A parallel-plate capacitor has plates of area 10 cm2 separated by a 0.10-mm layer of glass insulation with resistivity r = 1.2x1013 Ω m and dielectric constant k = 5.6. Because of the finite resistivity, charge leaks through the insulation.(a) How can such a leaky capacitor be represented in a
Obtain an expression for the rate of increase (dV/dt) of the voltage across a charging capacitor in an RC circuit. Evaluate your result at time t = 0, and show that if the capacitor continued charging steadily at this rate, it would reach full charge in exactly one time constant.
A 270Ω resistor is connected across a battery and a 31-mA current flows. When the resistor is replaced with a 120Ω resistor, the current increases to 63-mA. Find(a) the battery’s voltage(b) its internal resistance.
Show that only half the total energy drawn from a battery in charging an RC circuit ends up stored in the capacitor.
You’re writing the instruction manual for a stereo amplifier with a maximum output of 100 W. The amplifier can be modeled as an emf in series with an 8Ω resistance. What should you specify for the loudspeaker resistance to be used with the amplifier? How much power can the amplifier deliver to
Show that a battery delivers the most power when the load resistance across its terminals is equal to its internal resistance.
Suppose the currents into and out of a circuit node differ by 1 μA. If the node consists of a small metal sphere with diameter 1 mm, how long would it take for the electric field around the node to reach the 3-MV/m breakdown field in air?
Find the resistance needed in an RC circuit to bring a 20μf capacitor from zero charge to 45% charge in 140 ms.
The voltage on a charged capacitor is monitored with a voltmeter whose resistance is 1.00 MΩ. The table below gives the meter reading as a function of time. Determine a function of the voltage which, when you plot it against time, should give a straight line. Make your plot, establish a best-fit
An ammeter with resistance 1.42 Ω is connected momentarily across a battery, and the meter reads 9.78 A. When the measurement is repeated with a 2.11Ω meter, the reading is 7.46 A. Find(a) the battery voltage(b) its internal resistance.
A battery’s voltage is measured using a voltmeter with resistance 10.00 kΩ; the result is 4.982 V. A 15.00kΩ meter gives 4.993 V. Find(a) the battery’s voltage(b) its internal resistance.
A capacitor is charged until it holds 5.0 J of energy, then connected across a 10kΩ resistor. In 8.6 ms, the resistor dissipates 2.0 J.Find the capacitance.
A capacitor used to provide steady voltages in the power supply of a stereo amplifier charges rapidly to 35 V every 1/60 second. It must then hold that voltage to within 1.0 V for the next 1/60 s while it discharges through the amplifier. If the amplifier draws 1.2 A from the 35-V supply, (a)
You’re designing an external defibrillator that discharges a capacitor through the patient’s body, providing a pulse that stops ventricular fibrillation. Specifications call for a capacitor storing 250 J of energy; when discharged through a body with 40Ω transthoracic resistance, the
The voltage across a charging capacitor in an RC circuit rises to 1 - 1/e of the battery voltage in 5.0 ms.(a) How long will it take to reach 1 - 1/e3 of the battery voltage?(b) If the capacitor is charging through a 22kΩ resistor, what’s the capacitance?
A resistor draws 1.00 A from an ideal 12.0-V battery.(a) If an ammeter with 0.10Ω resistance is inserted in the circuit, what will it read?(b) If this current is used to calculate the resistance, by what percent will the result be in error?
How many 100-W, 120-V lightbulbs can be connected in parallel before they trip a 20-A circuit breaker?
A 6.0-V battery has internal resistance 2.5 Ω. If the battery is short-circuited, what’s the rate of energy dissipation in its internal resistance?
Your company is overstocked on 50Ω, 1 2-W resistors. Your project requires 50Ω resistors that can be safely connected across a 12-V power source. How many of the available resistors will you need, and how will you connect them?
A partially discharged car battery can be modeled as a 9-V emf in series with a 0.08Ω internal resistance. Jumper cables connect this battery to a fully charged battery, modeled as a 12-V emf in series with a 0.02Ω internal resistance. The cables connect + to + and - to -. What current flows
Three 1.5-V batteries, with internal resistances 0.01 Ω, 0.1 Ω, and 1 Ω, each have 1Ω resistors connected across their terminals. What’s the voltage between each battery’s terminals, to three significant figures?
An uncharged 10μF capacitor and a 470kΩ resistor are in series, and 250 V is applied across the combination. How long does it take the capacitor voltage to reach 200 V?
Show that a capacitor is charged to approximately 99% of the applied voltage in five time constants 15RC2.
If capacitance is in μF, what will be the units of the time constant RC when resistance is in(a) Ω,(b) kΩ,(c) MΩ?
Show that the quantity RC has the units of time (seconds).
A new mechanic foolishly connects an ammeter with 0.1Ω resistance directly across a 12-V car battery with internal resistance 0.01 Ω. What’s the power dissipation in the meter?
Find all three currents in the circuit of Fig. 25.13, but now with ?2 = 1.0 V. E = 6 V E = 9 V R = 20R3 = 1n R2 = 40 (a) Node A, Ra (Loops Loop! Node B Loop 3 (b)
You have a 1.0Ω, a 2.0Ω, and a 3.0Ω resistor. What equivalent resistances can you form using all three?
When a 9-V battery is temporarily short-circuited, a 200-mA current flows. What’s the battery’s internal resistance?
A defective starter motor draws 300 A from a car’s 12-V battery, dropping the battery terminal voltage to 6 V. A good starter should draw only 100 A. What will the battery terminal voltage be with a good starter?
What resistance should you place in parallel with a 56kΩ resistor to make an equivalent resistance of 45 kΩ?
A 47kΩ resistor and a 39kΩ resistor are in parallel, and the pair is in series with a 22kΩ resistor. What’s the resistance of the combination?
What resistance should you place in parallel with a 56kΩ resistor to make an equivalent resistance of 45 kΩ?
If you accidentally leave your car headlights (current 5 A) on for an hour, how much energy drains from the car’s 12-V battery?
A 1.5-V battery stores 4.5 kJ of energy. How long can it light a flashlight bulb that draws 0.60 A?
What’s the emf of a battery that delivers 27 J of energy as it moves 3.0 C between its terminals?
Resistors R1 and R2 are in series, and the series combination is in parallel with R3. This parallel combination is connected across a battery. Draw a diagram of this circuit.
Sketch a diagram for a circuit consisting of two batteries, a resistor, and a capacitor, all in series. Does the circuit description allow you any flexibility?
Sketch a circuit diagram for a circuit that includes a resistor R1 connected to the positive terminal of a battery, a pair of parallel resistors R2 and R3 connected to the lower-voltage end of R1 and then returned to the battery’s negative terminal, and a capacitor across R2.
A brownout occurs when an electric utility can’t supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity.
A brownout occurs when an electric utility can’t supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity.
A brownout occurs when an electric utility can’t supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity.
A brownout occurs when an electric utility can’t supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity.
You work for an automobile manufacturer developing a new plug-in hybrid car. The car’s mass is 1200 kg, and it uses a 360-V battery driving an electric motor that can handle a maximum current of 180 A. You’re to specify the greatest slope the car can climb, maintaining 60 km/h, without its
A cylindrical resistor is 5.0 mm in diameter and 1.5 cm long. It’s made of a composite material whose resistivity varies from one end to the other according to the equation ρ = ρ0(1 + x/L)ex/L , for 0 ≤x ≤ L, where ρ0 = 2.41 x 10-3 Ω m. Find its resistance.
The current density in a particle beam with circular cross section of radius a points along the beam axis with a magnitude that decreases linearly from J0 at the center (r = 0) to half that value at the edge (r = a). Find an expression for the total current in the beam.
Each atom in aluminum contributes about 3.5 conduction electrons. Find the drift speed in a 2.1-mm-diameter aluminum wire carrying 20 A.
An immersion-type heating coil is connected to a 120-V outlet and immersed in a 250-mL cup of water initially at 10°C. The water comes to a boil in 85 s. Assuming no heat loss, and neglecting the heater’s mass, find(a) the power(b) the heater’s resistance.
A metal bar has rectangular cross section 5.0 cm by 10 cm, as shown in Fig. 24.18. The bar has a nonuniform conductivity, and as a result the current density increases linearly from zero at the bottom to 0.10 A/cm2 at the top. Find the total current in the bar. 5.0 cm J= 0.10 A/cm 10 cm J = 0
A 240-V electric motor is 90% efficient, meaning that 90% of the energy supplied to it ends up as mechanical work. If the motor lifts a 200-N weight at 3.1 m/s, how much current does it draw?
You’re estimating costs for a new power line with your company’s financial group. Engineering specifies a resistance per unit length of 50 mΩ/km. The costs of copper and aluminum wire are $4.65/kg and $2.30/kg and their densities are 8.9 g/cm3 and 2.7 g/cm3, respectively. Which material is
A power plant produces 1000 MW to supply a city 40 km away. Current flows from the power plant on a single wire with resistance 50 mΩ/km, through the city, and returns via the ground, which has negligible resistance. At the power plant the voltage between wire and ground is 115 kV. Find(a) the
A 100%-efficient electric motor is lifting a 15-N weight at 25 cm/s. How much current does it draw from a 6.0-V battery?
You’re working on a new high-speed rail system. It uses 6000-horsepower electric locomotives, getting power from a single overhead wire with resistance 15 mΩ/km, at 25 kV potential relative to the track. Current returns through the track, whose resistance is negligible. Energy-efficiency
Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one dissipates twice as much power as the other. How do their diameters compare?
A thermally insulated container of seawater carries a uniform current density of 75 mA/cm2. How long does it take for its temperature to increase from 15°C to 20°C? Use the result of the preceding problem and any other information you might look up.
At a particular point in a material with resistivity ρ the current density has magnitude J. Show that the power per unit volume dissipated at this point is J2ρ.
Magnetic effects involving Jupiter’s moon Io result in an effective voltage of about 400 kV, which drives current of some 5 MA between Io and Jupiter’s polar regions. At Jupiter the current produces auroras analogous to those on Earth, as well as powerful bursts of radio waves that help radio
The Nissan Leaf is an all-electric car powered by a 107-hp electric motor and a lithium-ion battery that stores 24 kWh and produces 394 V at its terminals when fully charged. The Leaf’s battery can charge at the rate of 3.3 kW from a standard 120-V power outlet, at 6.6 kW from a 240-V outlet, and
A solid rectangular iron bar measures 0.50 cm by 1.0 cm by 20 cm. Find the resistance between each of the three pairs of opposing faces, assuming the faces in question are equipotentials.
An implanted pacemaker supplies the heart with 72 pulses per minute, each pulse providing 6.0 V for 0.65 ms. The resistance of the heart muscle between the pacemaker’s electrodes is 550 Ω. Find(a) the current that flows during a pulse,(b) the energy delivered in one pulse,(c) the average power
You’re writing the instruction manual for a power saw, and you have to specify the maximum permissible length for an extension cord made from 18-gauge copper wire (diameter 1.0 mm). The saw draws 7.0 A and needs a minimum of 115 V across its motor when the outlet supplies 120 V. What do you
How must the diameters of copper and aluminum wire be related if they’re to have the same resistance per unit length?
You have a cylindrical piece of material 2.4 cm long and 2.0 mm in diameter. When you attach a 9-V battery to its ends, a 2.6-mA current flows. Which material from Table 24.1 do you have?
Silver and iron wires of the same length and diameter carry the same current. How do the voltages across the two compare?
The maximum safe current in 12-gauge (2.1-mm-diameter) copper wire is 20 A. Find(a) the current density(b) the electric field under these conditions.

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