Chapter 18.1 - Coulomb’s Law

Chapter 18.1 - Coulomb’s Law

Assume gravity, tension and the electric force are all important in this problem. A small sphere of mass 7.50 grams and charge q1 = 32.0 nC is attached to the end of a string and hangs vertically as shown below. A second charge of equal mass and charge q2 = -58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge.

(a) How many excess electrons are present in charge q2?(b) What is the tension in the string, assuming both gravity and the electric force are significant?(c) If the string can withstand a maximum tension of 0.180 N, what is the smallest possible value of d before the string breaks?


Calculate the magnitude and direction of the electric force and each of the three charges below.


In the figure below, the negative charge is at the origin. Determine the point along the x-axis (other than infinity) at which the total electric field is zero.

Chapter 18.4 - Electric Fields

Three charges are arranged as shown. Find the magnitude and direction of the electric force on each of the two positive charges.


Three charges are at the corners of an equilateral triangle, as shown below. Calculate the magnitude and direction of the electric field at a point midway between the two charges on the x-axis (you will need to do some trig to find the height of the triangle).


Three charges are at the corners of an equilateral triangle, as shown below. (a) Calculate the magnitude and direction of the electric field due to the two positive charges at the location of the negative charge. (b) Determine the magnitude and direction of the total electric force acting on the negative charge.

Chapter 19.1 - Electric Potential and Potential Energy (Uniform Fields)

A proton is released from rest at x = -2.00 cm in a uniform electric field with magnitude 1000 N/C in the +x direction. (a) Calculate the change in electric potential energy associated with the proton when it reaches x = 5.00 cm. (b) If the potential at the initial position of the problem is exactly 0 Volts, what is the potential at x = 5.00 cm? (c) How much work is done by the electric force on the proton? (d) With what velocity must we fire an electron from x = -2.00 cm if it is to come to rest briefly at x = 5.00 cm? (e) How much work is done by the electric field on the electron?

Chapter 19.2 - Electric Potential and Potential Energy (Uniform Fields)

Assume only gravity and the electric force are important in this problem. A 2.00-kg ball with a charge of +462 μC is thrown upward from ground level with an initial speed of 35.0 m/s. Assume a uniform gravitational field (g = 9.8 m/s2) and a uniform electric field. The ball reaches a maximum height of 64.2 meters above ground level. (a) In what direction does the electric field point? (b) Is the voltage higher or lower at the maximum height compared to ground level? (c) If the voltage at ground level is 25,000 Volts, what is the voltage at the maximum height of the ball?

Chapter 19.3 - Electric Potential and Potential Energy (Non-uniform Fields)

Three charges are arranged at the corners of a rectangle as shown. (a) Find the electric potential for the upper right corner of the rectangle below. (b) Assuming a 4th charge of -5.00 μC is carried by an applied force from a very distant point and placed in the upper right corner of the rectangle, with the charge starting and ending its motion at rest, how much work does the applied force do?


An alpha particle (with charge +2e and mass of 6.64 x 10-27 kg) is fired toward a gold nucleus (charge +79e) from very far away with a speed of 2.00 x 107 m/s directly toward the nucleus. Assuming the gold nucleus remains fixed in place, how close does the alpha particle get to the gold nucleus before turning around?


A -75.0 µC charge is located at the origin and fixed in place. A 22.0-gram mass with a charge of -135 µC is located at x = 17.5 cm and initially at rest. An experimenter picks up the mass and places it (at rest) at x = 87.5 cm. You may assume that the electric force and the applied force of the experimenter are the only relevant forces here.

a) How much work is done by the experimenter?b) If the experimenter did not intervene and simply allowed the mass to accelerate on its own in

response to the electric force, how fast would the mass be moving at x = 87.5 cm?

Chapter 19.6 - Capacitors

When a 9.0 Volt battery is connected to the plates of a capacitor, it stores a charge of 27.0 µC. (a) What is the value of the capacitance? (b) How much electrical energy is stored by the capacitor? (c) If the plate separation is 3.50 mm, what is the electric field between the plates? (d) If a proton is released from rest from the positive plate, with what speed does it strike the negative plate?

Chapter 19.7 - Capacitors

A capacitor has a plate area of 5.00 cm2 and it is charged up by a power source so that an electric field of 180,000 Volts/meter exists between the plates, then it is disconnected from the source. (a) What is the charge on the positive plate? (b) If the plate separation is 1.5 mm, what is the potential difference between the plates? (c) Keeping in mind that the capacitor is disconnected from its voltage source, what happens to the potential difference between the plates if a K = 2.0 dielectric is inserted between the plates? (d) After the dielectric is inserted, the capacitor is reconnected to the power source, restoring the full potential difference to the plates that we found in part (b). What is the charge on the positive plate now?

Chapter 20.1 - Ohm’s Law

Nichrome wire (with resistivity 1.00 x 10-6 Ω-m) with a cross-sectional radius of 0.791 mm is used in winding a heating coil. The coil must carry a current of 9.25 Amps when a voltage of 120 Volts is applied across its ends. Find (a) the required resistance of the coil and (b) the length of wire needed to wind the coil.

Chapter 20.2 - Electrical Power

If electrical energy costs 12 cents per kilowatt-hour, how much does it cost to (a) light a 100-Watt light bulb for 24 hours? (b) Operate an electric oven for 5.0 hours if it carries a current of 20.0 A with a voltage of 220 Volts? (c) Operate a 4200 Watt air conditioning unit for 18 hours?

Chapter 20.3 - Series and Parallel Circuits

Three 9.0 Ohm resistors are connected in series with a 12 Volt battery. (a) Draw a circuit diagram for this setup, then find (b) the equivalent resistance of the circuit and (c) the current in each resistor.

Now the three resistors are connected in parallel across the battery. (a) Draw a circuit diagram for this setup, then find (b) the equivalent resistance of the circuit and (c) the current in each resistor.


Find the current through each resistor in the diagram below.


Consider the two arrangements shown below. The bulbs are identical and so are the batteries.

(a) Which bulb is brighter, bulb A in case 1 or case 2? Explain.(b) Which case has the most total power output? Explain.(c) Consider case 2 only. A third bulb C is added to the circuit, in series with and on the same

branch as bulb B. (i) What happens to the brightness of bulbs A and B when bulb C is added?(ii) Which bulb burns brighter, A or B, or are they the same? Explain.(iii) Which branch has a higher power output, A or BC?

Chapter 20.6 - Capacitors and RC Circuits

Consider a series RC circuit for which R = 75.0 Ω, C = 25.0 µF and 𝜀 = 12.0 V. A switch is closed at t = 0 to allow the initially uncharged capacitor to begin charging. (a) Find the charge on the capacitor after 3.00 ms have elapsed, (b) Find the current in the circuit at this time. (c) Find the charge on the capacitor after 2.00 time constants have elapsed.(d) What is the maximum possible charge on the capacitor?(e) At what time is the capacitor 95% charged?(f) How many time constants have elapsed when the capacitor is 95% charged?

Chapter 21.1 - Charged particles in magnetic fields

(Ch 21, #3) At a certain location, the horizontal component of the earth’s magnetic field is 2.5 x 10-5 T, due north. A proton moves eastward with just the right speed for the magnetic force on it to balance the weight of the proton, and there are no other forces acting on the proton. Find the speed of the proton.

(Ch 21, #11) The electrons in the beam of a television tube have a kinetic energy of 2.40 x 10-15 J. Initially, the electrons move horizontally from west to east. The vertical component of the earth’s magnetic field points down, toward the surface of the earth, and has a magnitude of 20.0 μT.

(a) In what direction are the electrons deflected by this field component?(b) What is the magnitude and direction of the acceleration of the electron in part a?


(Ch 21, #15) A charged particle enters a uniform magnetic field and follows the circular path shown below.

(a) Is the particle positively or negatively charged? Why?(b) The particle’s speed is 140 m/s, the magnitude of the magnetic field is 0.48 T, and the radius

of the path is 960 m. Determine the mass of the particle, given that its charge has a magnitude of 8.2 x 10-4 C.


Consider the mass spectrometer shown schematically below. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930 T. Calculate the radius of the path in the system for a singly-charged ion with mass m = 2.18 x 10-26 kg.

Chapter 21.4 - Currents and Current Loops in Magnetic Fields

(Ch 21, #33) A horizontal wire of length 0.53 m, carrying a current of 7.5 A, is placed in a uniform external magnetic field. When the wire is parallel to Earth’s surface (horizontal) and the current is running along the wire toward the North, it experiences no magnetic force. When the wire is tilted upward at an angle of 19° above the horizontal (and above North in the plane of the Earth’s surface), it experiences a magnetic force of 0.0044 N due East. What is the magnitude and direction of the magnetic field the wire is immersed in?

Chapter 21.5 - Currents and Current Loops in Magnetic Fields

(Ch 21, #43) The 1200-turn coil in a dc motor has an area per turn of 0.011 m2. The design for the motor specifies that the magnitude of the maximum torque is 5.8 N·m when the coil is placed in a 0.20-T magnetic field. What is the current in the coil?

Chapter 21.6 - Magnetic fields generated by currents and current loops

(Ch 21, #59) Two long, straight wires are separated by 0.120 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates. Find the magnitude and direction of the net magnetic field at the points labeled A and B.


Two long, parallel wires carry currents of I1 = 3.00 A and I2 = 5.00 A as indicated below. Find the magnitude and direction of the net magnetic field at point P, located d = 20.0 cm above the wire carrying the 5.00 A current.


The current in the long, straight wire is I1 = 5.00 A, and the wire lies in the plane of the rectangular loop, which carries a current of 10.0 A. The dimensions shown are c = 0.100 m, a = 0.150 m and = 0.450 m. Find the magnitude and direction of the net force exerted by the magnetic field of the straight wire on the rectangular loop.

Chapter 22.1 - Motional EMF

(Ch 22, #1) A 0.80-m Aluminum bar is held with its length parallel to the east-west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 22 m/s, and the EMF induced across its length is 6.5 x 10-4 Volts. Assuming the horizontal component of earth’s magnetic field at the location of the bar points directly north,

(a) determine the magnitude of the horizontal component of earth’s magnetic field(b) state whether the east end or the west end of the bar is positive.

Chapter 22.2 - Motional EMF

(Ch 22, #5) The drawing shows three identical rods (A, B and C) moving in different planes. A constant magnetic field of magnitude 0.45 T is directed along the +y axis. The length of each rod is L = 1.3 m, and the rods each have the same speed of 2.7 m/s. For each rod, find the magnitude of the motional EMF, and indicate which end (1 or 2) of the rod is positive.

Chapter 22.3 - Magnetic Flux and Induction

(Ch 22, #21) A circular coil (950 turns, radius 0.060 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle Φ = 45° with the field because the coil has made one-eighth of a revolution. An average emf of magnitude 0.065 Volts is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.

(Ch 22, #72) A planar coil of wire has a single turn. The normal to this coil is parallel to a uniform and constant (in time) magnetic field of 1.7 T. An emf that has a magnitude of 2.6 Volts is induced in this coil because the coil’s area A is shrinking. What is the magnitude of ∆A/∆t, which is the rate (in m2/s) at which the area changes?


(Ch 22, #79) A piece of copper wire is formed into a single circular loop of radius 12 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.60 T in a time of 0.45 s. The wire has a resistance per unit length of 0.033 Ω/m. What is the average electrical energy dissipated by the resistance of the wire?


(Ch 22, #34) The drawing below shows a straight wire carrying a current I. Above the wire is a rectangular loop that contains a resistor R. If the current is decreasing in time, what is the direction of the induced current through the resistor R — left-to-right or right-to-left? Explain.

Chapter 24.1 - Properties of Light

(Ch 24, #10) FM radio waves have frequencies between 88.0 and 108.0 MHz. (a) Determine the range of wavelengths for these waves. (b) Determine the range also for the AM band, which extends from about 530 to 1730 kHz.


(Ch 24, #27) A neodymium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field of such a wave has an rms value of Erms = 2.0 x 109 N/C. Find the average power of each pulse that passes through a 0.16 cm2 surface that is perpendicular to the beam.


(Ch 24, #2) Neil Armstrong was the first person to walk on the moon. The distance between the earth and the moon at a certain time is 3.85 x 108 m. (a) Find the time it would take for his voice to reach the earth via radio waves at that distance. (b) Someday a person will walk on Mars, which is 5.6 x 1010 m from the earth at the point of closest approach (also called “opposition”). Determine the minimum time that will be required for a message from Mars to reach the earth via radio waves.


A 75-Watt light bulb attached to a dark-colored (light absorbing) ceiling radiates half of its power uniformly over a hemispherical region. Half of its power radiates into the ceiling and is absorbed. At a distance of 3.5 meters away from the bulb, what is

a) the average intensity of the lightb) the rms value of the electric field due to the lightc) the energy density of the light

Chapter 24.5 - Doppler Shift

The drawing below shows three situation in which an observer and a source are moving along the same line. In each case, the source emits a wave with a frequency of 4.5 x 1014 Hz. The arrows indicate speed relative to rest, where v = 1.2 x 106 m/s. Calculate the observed frequency in each case.

Chapter 24.6 - Doppler Shift

A car approaches a police radar gun. The radar gun emits an electromagnetic wave with a frequency of 7.0 GHz. Upon reflecting off the approaching car, the frequency of the reflected wave is greater by 2100 Hz. What is the speed of the approaching car?

Note that due to reflection, the Doppler effect is doubled. This means you can approximate by saying the car reflects 7.0 GHz back to the officer, but you also assume the car’s speed for the calculation is double its true value (see the full solution to chapter 24, problem 63 for the algebra involved) to find the new frequency for the reflected light as measured by the radar gun.

Chapter 24.7 - Polarization

(Ch 24, #43) Suppose that unpolarized light of intensity 150 W/m2 falls on the vertically oriented polarizer shown below, and the angle θ in the drawing is 30.0°. What is the light intensity reaching the photocell? Assume the final polarizer is oriented horizontally.

Chapter 25.1 - Light and Mirrors

(Ch 25, #5) The drawing shows two plane mirrors that intersect at an angle of 120°. An incident light ray reflects from one mirror and then the other. What is the angle θ of the reflected ray from the mirror M2?

Chapter 25.2 - Light and Mirrors

(Ch 25, #6) The drawing below shows a laser beam shining on a plane mirror that is perpendicular to the ground. How far from the base of the mirror does the beam strike the floor?

Chapter 25.3 - Spherical Mirrors and Images

(Ch 25, #16) A 2.0-cm high object is situated 15.0 cm in front of a concave mirror that has a radius of curvature of 10.0 cm. What is (a) the location and (b) the height of the image?


(Ch 25, #22) A small statue has a height of 3.5 cm and is placed in front of a concave mirror. The image of the statue is inverted, 1.5 cm tall, and located 13 cm in front of the mirror. Find the focal length of the mirror.


(Ch 25, #33) A concave makeup mirror is designed so that the virtual image it produces is twice the size of the object when the distance between the object and the mirror is 14.0 cm. What is the radius of curvature of the mirror?

Chapter 26.1 - Refraction of Light

(Ch 26, #13) The drawing shows a coin resting on the bottom of a beaker filled with an unknown liquid. A ray of light from the coin travels to the surface of the liquid and is refracted as it enters into the air. A person sees the ray as it skims just above the surface of the liquid. How fast is the light traveling in the liquid?


The light beam shown below strikes surface 2 at the critical angle. Determine the angle of incidence, θ1.


(Ch 26, #37) Light is reflected from a glass coffee table. When the angle of incidence is 56.7°, the reflected light is completely polarized parallel to the surface of the glass. What is the index of refraction of the glass?

Chapter 26.4 - Lenses and Images

(Ch 26, #53) A slide projector has a converging lens whose focal length is 10.5 cm.

(a) How far (in meters) from the lens must the screen be located if a slide is placed 10.8 cm from the lens?

(b) If the slide measures 24.0 mm x 36.0 mm, what are the dimensions of its image?


(Ch 26, #57) A converging lens has a focal length of 88.0 cm. A real object 13.0 cm tall creates an inverted real image with a height of 17 cm. What is the image distance?


(Ch 26, #60) When a converging lens is used in a camera, the film must be at a distance of 0.210 m from the lens to record an image of an object that is 4.00 m from the lens. The same lens and film are used in a projector, with the screen 0.500 m from the lens. How far from the projector lens should the film be placed?


(Ch 26, #68) A converging lens (f1 = 24.0 cm) is located 56.0 cm to the left of a diverging lens (f2 = -28.0 cm). An object is placed to the left of the converging lens, and the final image produced by the two-lens combination is 20.7 cm to the left of the diverging lens. How far is the object from the converging lens?

Chapter 26.8 - The Human Eye

(Ch 26, #77) Your friend has a near point of 138 cm, and she wears contact lenses that have a focal length of 35.1 cm. How close can she hold a magazine and still read it clearly?

Chapter 27.1 - Double Slit Interference

(Ch 27, #1) In a double-slit experiment, the wavelength of the light used is 520 nm (in vacuum), and the separation between the slits is 1.4 x 10-6 m. Determine the angle that locates:

(a) the dark fringe for which m = 0 (the zeroth order dark fringe)(b) the bright fringe for which m = 1 (the first order bright fringe)(c) the dark fringe for which m = 1 (the first order dark fringe)(d) the bright fringe which which m = 2 (the second order bright fringe)

Chapter 27.2 - Thin Film Interference

(Ch 27, #13) A non reflective coating of magnesium fluoride (n = 1.38) covers the glass (n = 1.52) of a camera lens. Assuming that the coating prevents reflection of yellow-green light (wavelength in vacuum = 565 nm), determine the minimum nonzero thickness that the coating can have.

Chapter 27.3 - Thin Film Interference

A 455-nm thick anti-reflective coating (n = 1.52) is applied to a smooth glass surface (n = 1.44). What wavelengths of light in the visible region of the spectrum (between 400 and 700 nm) are brightly reflected from this surface? Be show to show all steps in solving this problem?

Chapter 27.4 - Single Slit Interference and Resolving Power

(Ch 27, #27) Light that has a wavelength of 668 nm passes through a slit 6.73 x 10-6 m wide and falls on a screen that is 1.85 m away. What is the width (in mm) of the central maximum of the single slit pattern?

Chapter 27.5 - Single Slit Interference and Resolving Power

A large refracting telescope has an objective lens with a diameter of 1.02 m. Two objects are 3.03 km from the telescope. With light of wavelength 569 nm, how close can the objects be to each other so that they are just barely resolved by the telescope?

Chapter 27.6 - Diffraction Gratings

(Ch 27, #45) For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 41°. In both cases, the bright fringes are of the same order m. What is the unknown wavelength?

Chapter 29.1 - The Photoelectric Effect

(Ch 29, #9) An owl has good night vision because its eyes can detect a light intensity as small as 5.0 x 10-13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5 mm and the light has a wavelength of 510 nm?

Chapter 29.2 - The Photoelectric Effect

(Ch 29, #3) Ultraviolet light with a frequency of 3.00 x 1015 Hz strikes a metal surface and ejects electrons that have a maximum kinetic energy of 6.1 eV. What is the work function (in eV) of the metal?

Chapter 29.3 - Momentum of a Photon

A small reflecting cube with a mass about equal to a ping-pong ball (mass = 2.2 grams) is sliding across a frictionless surface with a speed of 0.25 m/s. A student shines a high power laser (wavelength = 522 nm) at the cube to try to stop it. Assume that since the photons are reflecting, they deliver twice their momentum to the cube.

a) How many photons must reflect off of the cube in order for the cube to stop?b) Assume it takes 45 seconds to the stop the cube, what must be the power of the laser (in

Watts)?

Chapter 30.1 - Spectral Absorption and Emission

(Ch 30, #11) Find the energy (in joules) of the photon that is emitted when the electron in a hydrogen atom undergoes a transition from the n = 7 energy level to produce a line in the Paschen series.

(Ch 30, #55) In the line spectrum of atomic hydrogen there is also a group of lines known as the Pfund series. These lines are produced when electrons, excited to high energy levels, make transitions to the n = 5 level. Determine (a) the longest wavelength and (b) the shortest wavelength in the series.

Chapter 31.1 - Nuclear Physics

(Ch 31, #11) Find the binding energy (in MeV) for 7Li (atomic mass = 7.016003 u).

Chapter 31.2 - Radioactivity

(Ch 31, #32) In 9.0 days the number of radioactive nuclei decreases to one-eighth the number present initially. What is the half-life (in days) of the material?

(Ch 31, #37) Suppose that the activity of a radioactive substance is initially 398 disintegrations per minute, and two days later, it is 285 disintegrations per minute. What is the activity six days after the initial sample is measured (answer in disintegrations per minute)?

Chapter 31.3 - Radioactivity

(Ch 31, #41) A device used in radiation therapy for cancer contains 0.50 g of Cobalt-60(59.933819 u). The half-life of 60Co is 5.27 years. Determine the activity of the radioactive material.

Chapter 18.1 - Coulomb’s Law

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