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physics
mechanics
Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions
A cell membrane has a surface area of 1.0 × 10−7 m2, a dielectric constant of 5.2, and a thickness of 7.5 nm. The membrane acts like the dielectric in a parallel plate capacitor; a layer of positive ions on the outer surface and a layer of negative ions on the inner surface act as the capacitor
An axon has the outer part of its membrane positively charged and the inner part negatively charged. The membrane has a thickness of 4.4 nm and a dielectric constant k = 5. If we model the axon as a parallel plate capacitor whose area is 5 μm2, what is its capacitance?
An electron beam is deflected upward through 3.0 mm while traveling in a vacuum between two deflection plates 12.0 mm apart. The potential difference between the deflecting plates is 100.0 kV and the kinetic energy of each electron as it enters the space between the plates is 2.0 ×
A point charge q = − 2.5nC is initially at rest adjacent to the negative plate of a capacitor. The charge per unit area on the plates is 4.0μC/m2 and the space between the plates is 6.0 mm. (a) What is the potential difference between the plates? (b) What is the kinetic energy of the point
An alpha particle (helium nucleus, charge + 2e) starts from rest and travels a distance of 1.0 cm under the influence of a uniform electric field of magnitude 10.0 kV/m. What is the final kinetic energy of the alpha particle?
The inside of a cell membrane is at a potential of 90.0 mV lower than the outside. How much work does the electric field do when a sodium ion (Na+) with a charge of + e moves through the membrane from outside to inside?
Draw some electric field lines and a few equipotential surfaces outside a positively charged metal cube.
A parallel plate capacitor is attached to a battery that supplies a constant voltage. While the battery remains attached to the capacitor the distance between the parallel plates increases by 25%. What happens to the energy stored in the capacitor?
In the diagram, how much work is done by the electric field as a third charge q3 = + 2.00nC is moved from infinity to point a?
A parallel plate capacitor is attached to a battery that supplies a constant voltage. While the battery is still attached, a dielectric of dielectric constant k = 3.0 is inserted so that it just fits between the plates. What is the energy stored in the capacitor after the dielectric is inserted in
(a) Calculate the capacitance per unit length of an axon of radius 5.0 μ m (Fig. 17.14). The membrane acts as an insulator between the conducting fluids inside and outside the neuron. The membrane is 6.0 nm thick and has a dielectric constant of 7.0. (b) In its resting state (no signal being
A 4.00-μF air gap capacitor is connected to a 100.0-V battery until the capacitor is fully charged. The battery is removed and then a dielectric of dielectric constant 6.0 is inserted between the plates without allowing any charge to leak off the plates. (a) Find the energy stored in the
It has only been fairly recently that 1.0-F capacitors have been readily available. A typical 1.0-F capacitor can withstand up to 5.00 V. To get an idea why it isn't easy to make a 1.0-F capacitor, imagine making a 1.0-F parallel plate capacitor using titanium dioxide (k = 90.0, breakdown strength
The potential difference across a cell membrane from outside to inside is initially at − 90 mV (when in its resting phase). When a stimulus is applied, Na + ions are allowed to move into the cell such that the potential changes to + 20 mV for a short amount of time. (a) If the membrane
A parallel plate capacitor is connected to a battery. The space between the plates is filled with air. The electric field strength between the plates is 20.0 V/m. Then, with the battery still connected, a slab of dielectric (k = 4.0) is inserted between the plates. The thickness of the dielectric
A point charge q = + 3.0 nC moves through a potential difference ΔV = Vf − Vi = + 25 V. What is the change in the electric potential energy?
An electron is moved from point A, where the electric potential is VA = − 240 V, to point B, where the electric potential is VB = − 360 V. What is the change in the electric potential energy?
Find the electric field and the potential at the center of a square of side 2.0 cm with charges of + 9.0μC at each corner.
Find the electric field and the potential at the center of a square of side 2.0 cm with a charge of + 9.0μC at one corner of the square and with charges of ˆ’ 3.0μC at the remaining three corners.
A charge Q = ˆ’ 50.0nC is located 0.30 m from point A and 0.50 m from point B.(a) What is the potential at A?(b) What is the potential at B?(c) If a point charge q is moved from A to B while Q is fixed in place, through what potential difference does it move? Does its potential increase or
A hydrogen atom has a single proton at its center and a single electron at a distance of approximately 0.0529 nm from the proton. (a) What is the electric potential energy in joules? (b) What is the significance of the sign of the answer?
A charge of + 2.0mC is located at x = 0, y = 0 and a charge of − 4.0mC is located at x = 0, y = 3.0 m. What is the electric potential due to these charges at a point with coordinates x = 4.0 m, y = 0?
A spherical conductor with a radius of 75.0 cm has an electric field of magnitude 8.40 × 10 5 V/m just outside its surface. What is the electric potential just outside the surface, assuming the potential is zero far away from the conductor?
An array of four charges is arranged along the x -axis at intervals of 1.0 m.(a) If two of the charges are + 1.0μC and two are ˆ’ 1.0μC, draw a configuration of these charges that minimizes the potential at x = 0.(b) If three of the charges are the same, q = +
At a point P, a distance R0 from a positive charge Q0, the electric field has a magnitude E0 = 100 N/C and the electric potential is V0 = 10 V. The charge is now increased by a factor of three, becoming 3Q0.(a) At what distance, RE, from the charge 3Q0 will the electric field have the same value, E
Charges of + 2.0nC and ˆ’ 1.0nC are located at opposite corners, A and C, respectively, of a square which is 1.0 m on a side. What is the electric potential at a third corner, B, of the square (where there is no charge)?
(a) Find the electric potential at points a and b for charges of + 4.2nC and ˆ’ 6.4nC located as shown in the figure.(b) What is the potential difference Δ V for a trip from a to b?(c) How much work must be done by an external agent to move a point charge of + 1.50nC from a to
(a) Find the potential at points a and b in the diagram for charges Q1 = + 2.50nC and Q2 = ˆ’ 2.50nC.(b) How much work must be done by an external agent to bring a point charge q from infinity to point b?
(a) In the diagram, what are the potentials at points a and b? Let V = 0 at infinity.(b) What is the change in electric potential energy if a third charge q3 = + 2.00nC is moved from point a to point b?
(a) In the diagram, what are the potentials at points b and c? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q 3 = + 2.00nC is moved from point b to point c?
How much work is done by an applied force that moves two charges of 6.5μC that are initially very far apart to a distance of 4.5 cm apart?
By rewriting each unit in terms of kilograms, meters, seconds, and coulombs, show that 1 N/C = 1 V/m.
A uniform electric field has magnitude 240 N/C and is directed to the right. A particle with charge + 4.2nC moves along the straight line from a to b.(a) What is the electric force that acts on the particle?(b) What is the work done on the particle by the electric field?(c) What is the potential
In a region where there is an electric field, the electric forces do + 8.0. 10−19 J of work on an electron as it moves from point X to point Y. (a) Which point, X or Y, is at a higher potential? (b) What is the potential difference, VY − VX, between point Y and point X?
Suppose a uniform electric field of magnitude 100.0 N/C exists in a region of space. How far apart are a pair of equipotential surfaces whose potentials differ by 1.0 V?
Draw some electric field lines and a few equipotential surfaces outside a negatively charged hollow conducting sphere. What shape are the equipotential surfaces?
Draw some electric field lines and a few equipotential surfaces outside a positively charged conducting cylinder. What shape are the equipotential surfaces?
It is believed that a large electric fish known as Torpedo occidental is uses electricity to shock its victims. A typical fish can deliver a potential difference of 0.20 kV for a duration of 1.5 ms. This pulse delivers charge at a rate of 18 C/s. (a) What is the rate at which work is done by the
A positive point charge is located at the center of a hollow spherical metal shell with zero net charge.(a) Draw some electric field lines and sketch some equipotential surfaces for this arrangement.(b) Sketch graphs of the electric field magnitude and the potential as functions of r.
If the electric force on the drop is found to be 9.6 × 10−16 N and the potential difference between the plates is 480 V, what is the magnitude of the charge on the drop in terms of the elementary charge e? Ignore the small buoyant force on the drop.
If the mass of the drop is 1.0 × 10−15 kg and it remains stationary when the potential difference between the plates is 9.76 kV, what is the magnitude of the charge on the drop? (Ignore the small buoyant force on the drop.)
The nucleus of a helium atom contains two protons that are approximately 1 fm apart. How much work must be done by an external agent to bring the two protons from an infinite separation to a separation of 1.0 fm?
Point P is at a potential of 500.0 kV and point S is at a potential of 200.0 kV. The space between these points is evacuated. When a charge of + 2e moves from P to S, by how much does its kinetic energy change?
An electron is accelerated from rest through a potential difference Δ V. If the electron reaches a speed of 7.26 × 106 m/s, what is the potential difference? Be sure to include the correct sign. (Does the electron move through an increase or a decrease in potential?)
As an electron moves through a region of space, its speed decreases from 8.50 × 106 m/s to 2.50 × 106 m/s. The electric force is the only force acting on the electron. (a) Did the electron move to a higher potential or a lower potential? (b) Across what potential difference did the electron
In the electron gun of Example 17.8, if the potential difference between the cathode and anode is reduced to 6.0 kV, with what speed will the electrons reach the anode?
In the electron gun of Example 17.8, if the electrons reach the anode with a speed of 3.0 × 107 m/s, what is the potential difference between the cathode and the anode?
A beam of electrons of mass m e is deflected vertically by the uniform electric field between two oppositely charged, parallel metal plates. The plates are a distance d apart and the potential difference between the plates is ΔV.(a) What is the direction of the electric field between
An electron (charge − e) is projected horizontally into the space between two oppositely charged parallel plates. The electric field between the plates is 500.0 N/C upward. If the vertical deflection of the electron as it leaves the plates has magnitude 3.0 mm, how much has its kinetic energy
An alpha particle (charge + 2e) moves through a potential difference ΔV = − 0.50 kV. Its initial kinetic energy is 1.20 × 10−16 J. What is its final kinetic energy?
In 1911, Ernest Rutherford discovered the nucleus of the atom by observing the scattering of helium nuclei from gold nuclei. If a helium nucleus with a mass of 6.68 × 10−27 kg, a charge of + 2 e, and an initial velocity of 1.50 × 107 m/s is projected head-on toward a gold nucleus with a charge
The figure shows a graph of electric potential versus position along the x -axis. A proton is originally at point A, moving in the positive x -direction. How much kinetic energy does it need to have at point A in order to be able to reach point E (with no forces acting on the electron other than
How much work does it take for an external force to set up the arrangement of charged objects in the diagram on the corners of a right triangle when the three objects are initially very far away from each other?
Repeat Problem 49 for an electron rather than a proton.
The plates of a 15.0-μF capacitor have net charges of + 0.75μC and − 0.75μC, respectively. (a) What is the potential difference between the plates? (b) Which plate is at the higher potential?
A parallel plate capacitor has a capacitance of 2.0 μF and plate separation of 1.0 mm. (a) How much potential difference can be placed across the capacitor before dielectric breakdown of air occurs (Emax = 3 × 106 V/m)? (b) What is the magnitude of the greatest charge the capacitor can store
A parallel plate capacitor has a capacitance of 1.20 nF. There is a charge of magnitude 0.800μC on each plate. (a) What is the potential difference between the plates? (b) If the plate separation is doubled, while the charge is kept constant, what will happen to the potential difference?
A parallel plate capacitor is connected to a 12-V battery. While the battery remains connected, the plates are pushed together so the spacing is decreased. What is the effect on? (a) The potential difference between the plates? (b) The electric field between the plates? (c) The magnitude of
A parallel plate capacitor has a capacitance of 1.20 nF and is connected to a 12-V battery. (a) What is the magnitude of the charge on each plate? (b) If the plate separation is doubled while the plates remain connected to the battery, what happens to the charge on each plate and the electric
A variable capacitor is made of two parallel semicircular plates with air between them. One plate is fixed in place and the other can be rotated. The electric field is zero everywhere except in the region where the plates overlap.When the plates are directly across from one another, the capacitance
What is the potential energy for these two charges?
Two metal spheres have charges of equal magnitude, 3.2 × 10−14 C, but opposite sign. If the potential difference between the two spheres is 4.0 mV, what is the capacitance?
Suppose you were to wrap the Moon in aluminum foil and place a charge Q on it. What is the capacitance of the Moon in this case?
A tiny hole is made in the center of the negatively and positively charged plates of a capacitor, allowing a beam of electrons to pass through and emerge from the far side. If 40.0 V are applied across the capacitor plates and the electrons enter through the hole in the negatively charged plate
A spherical conductor of radius R carries a total charge Q. (a) Show that the magnitude of the electric field just outside the sphere is E = σ/ϵ0, where s is the charge per unit area on the conductor's surface. (b) Construct an argument to show why the electric field at a point P just outside
A 6.2-cm by 2.2-cm parallel plate capacitor has the plates separated by a distance of 2.0 mm. (a) When 4.0 × 10−11 C of charge is placed on this capacitor, what is the electric field between the plates? (b) If a dielectric with dielectric constant of 5.5 is placed between the plates while the
Before a lightning strike can occur, the breakdown limit for damp air must be reached. If this occurs for an electric field of 3.33 × 105 V/m, what is the maximum possible height above the Earth for the bottom of a thundercloud, which is at a potential 1.00 × 108 V below Earth's surface
Two cows, with approximately 1.8 m between their front and hind legs, are standing under a tree during a thunderstorm. (a) If the equipotential surfaces about the tree just after a lightning strike are as shown, what is the average electric field between Cow A's front and hind legs? (b) Which cow
A parallel plate capacitor has a charge of 0.020μC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of bakelite. What is the capacitance of this capacitor?
Two metal spheres are separated by a distance of 1.0 cm and a power supply maintains a constant potential difference of 900 V between them. The spheres are brought closer to one another until a spark flies between them. If the dielectric strength of dry air is 3.0 × 106 V/m, what is the distance
What is the potential energy if a third point charge q = ˆ’ 4.2nC is placed at point a?
To make a parallel plate capacitor, you have available two flat plates of aluminum (area 120 cm2), a sheet of paper (thickness = 0.10 mm, k = 3.5), a sheet of glass (thickness = 2.0 mm, k = 7.0), and a slab of paraffin (thickness = 10.0 mm, k = 2.0). (a) What is the largest capacitance possible
A capacitor can be made from two sheets of aluminum foil separated by a sheet of waxed paper. If the sheets of aluminum are 0.30 m by 0.40 m and the waxed paper, of slightly larger dimensions, is of thickness 0.030 mm and dielectric constant k = 2.5, what is the capacitance of this capacitor?
In capacitive electro stimulation, electrodes are placed on opposite sides of a limb. A potential difference is applied to the electrodes, which is believed to be beneficial in treating bone defects and breaks. If the capacitance is measured to be 0.59 pF, the electrodes are 4.0 cm2 in area, and
A certain capacitor stores 450 J of energy when it holds 8.0 × 10−2 C of charge. What is (a) The capacitance of this capacitor (b) The potential difference across the plates?
What is the maximum electric energy density possible in dry air without dielectric breakdown occurring?
A parallel plate capacitor has a charge of 5.5 × 10−7 C on one plate and − 5.5 × 10−7 C on the other. The distance between the plates is increased by 50% while the charge on each plate stays the same. What happens to the energy stored in the capacitor?
A large parallel plate capacitor has plate separation of 1.00 cm and plate area of 314 cm2. The capacitor is connected across a voltage of 20.0 V and has air between the plates. How much work is done on the capacitor as the plate separation is increased to 2.00 cm?
Figure 17.31b shows a thundercloud before a lightning strike has occurred. The bottom of the thundercloud and the Earth's surface might be modeled as a charged parallel plate capacitor. The base of the cloud, which is roughly parallel to the Earth's surface, serves as the negative plate and the
A parallel plate capacitor of capacitance 6.0μF has the space between the plates filled with a slab of glass with k = 3.0. The capacitor is charged by attaching it to a 1.5-V battery. After the capacitor is disconnected from the battery, the dielectric slab is removed. Find(a) The
A parallel plate capacitor is composed of two square plates, 10.0 cm on a side, separated by an air gap of 0.75 mm. (a) What is the charge on this capacitor when there is a potential difference of 150 V between the plates? (b) What energy is stored in this capacitor?
The capacitor of Problem 79 is initially charged to a 150-V potential difference. The plates are then physically separated by another 0.750 mm in such a way that none of the charge can leak off the plates. Find (a) The new capacitance (b) The new energy stored in the capacitor. Explain the result
Capacitors are used in many applications where you need to supply a short burst of energy. A 100.0-μF capacitor in an electronic flash lamp supplies an average power of 10.0 kW to the lamp for 2.0 ms. (a) To what potential difference must the capacitor initially be charged? (b) What is its
A parallel plate capacitor has a charge of 0.020μC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of air. What energy is stored in this capacitor?
A parallel plate capacitor has a capacitance of 1.20 nF. There is a charge of 0.80μC on each plate. How much work must be done by an external agent to double the plate separation while keeping the charge constant?
A defibrillator is used to restart a person's heart after it stops beating. Energy is delivered to the heart by discharging a capacitor through the body tissues near the heart. If the capacitance of the defibrillator is 9μF and the energy delivered is to be 300 J, to what potential difference must
A defibrillator consists of a 15-μF capacitor that is charged to 9.0 kV. (a) If the capacitor is discharged in 2.0 ms, how much charge passes through the body tissues? (b) What is the average power delivered to the tissues?
The bottom of a thundercloud is at a potential of − 1.00 × 108 V with respect to Earth's surface. If a charge of − 25.0 C is transferred to the Earth during a lightning strike, find the electric potential energy released. (Assume that the system acts like a capacitor-as charge flows, the
(a) If the bottom of a thundercloud has a potential of − 1.00 × 109 V with respect to Earth and a charge of − 20.0 C is discharged from the cloud to Earth during a lightning strike, how much electric potential energy is released? (Assume that the system acts like a capacitor- as charge flows,
Charges of − 12.0nC and − 22.0nC are separated by 0.700 m. What is the potential midway between the two charges?
Two point charges (+ 10.0nC and ˆ’ 10.0nC) are located 8.00 cm apart.(a) What is the electric potential energy when a point charge of ˆ’ 4.2nC is placed at points a, b, and c in turn? Let U = 0 when the ˆ’ 4.2nC charge is far away (but the other two are still in
If an electron moves from one point at a potential of − 100.0 V to another point at a potential of + 100.0 V, how much work is done by the electric field?
A van de Graaff generator has a metal sphere of radius 15 cm. To what potential can it be charged before the electric field at its surface exceeds 3.0 × 106 N/C (which is sufficient to break down dry air and initiate a spark)?
Find the potential at the sodium ion, Na+, which is surrounded by two chloride ions, Clˆ’, and a calcium ion, Ca2+, in water as shown in the diagram. The effective charge of the positive sodium ion in water is 2.0 × 10ˆ’21 C, of the negative chlorine ion is
An infinitely long conducting cylinder sits near an infinite conducting sheet (side view in the diagram). The cylinder and sheet have equal and opposite charges; the cylinder is positive.(a) Sketch some electric field lines.(b) Sketch some equipotential surfaces.
Two parallel plates are 4.0 cm apart. The bottom plate is charged positively and the top plate is charged negatively, producing a uniform electric field of 5.0 × 104 N/C in the region between the plates. What is the time required for an electron, which starts at rest at the upper plate, to reach
The potential difference across a cell membrane is − 90 mV. If the membrane's thickness is 10 nm, what is the magnitude of the electric field in the membrane? Assume the field is uniform.
A beam of electrons traveling with a speed of 3.0 × 107 m/s enters a uniform, downward electric field of magnitude 2.0 × 104 N/C between the deflection plates of an oscilloscope. The initial velocity of the electrons is perpendicular to the field. The plates are 6.0 cm
A negatively charged particle of mass 5.00 × 10ˆ’19 kg is moving with a speed of 35.0 m/s when it enters the region between two parallel capacitor plates. The initial velocity of the charge is parallel to the plate surfaces and in the positive x -direction. The plates are
(a) Show that it was valid to ignore the gravitational force in Problem 97. In problem 97 A negatively charged particle of mass 5.00 × 10−19 kg is moving with a speed of 35.0 m/s when it enters the region between two parallel capacitor plates. The initial velocity of the charge is parallel to
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