The drawing shows a square, each side of which has a

During a particular thunderstorm, the electric potential diff erence between a cloud and the ground is Vcloud 2 Vground 5 1.3 3 108 V, with the cloud being at the higher potential. What is the change in an electrons electric potential energy when the electron moves from the ground to the cloud?

A particle with a charge of 21.5 mC and a mass of 2.5 3 1026 kg is released from rest at point A and accelerates toward point B, arriving there with a speed of 42 m/s. The only force acting on the particle is the electric force. (a) Which point is at the higher potential? Give your reasoning. (b) What is the potential diff erence VB 2 VA between A and B?

Suppose that the electric potential outside a living cell is higher than that inside the cell by 0.070 V. How much work is done by the electric force when a sodium ion (charge 5 1e) moves from the outside to the inside?

A particle has a charge of 11.5 mC and moves from point A to point B, a distance of 0.20 m. The particle experiences a constant electric force, and its motion is along the line of action of the force. The diff erence between the particles electric potential energy at A and at B is EPEA 2 EPEB 5 19.0 3 1024 J. (a) Find the magnitude and direction of the electric force that acts on the particle. (b) Find the magnitude and direction of the electric fi eld that the particle experiences.

Multiple-Concept Example 3 employs some of the concepts that are needed here. An electric car accelerates for 7.0 s by drawing energy from its 290-V battery pack. During this time, 1200 C of charge passes through the battery pack. Find the minimum horsepower rating of the car.

Review Multiple-Concept Example 4 to see the concepts that are pertinent here. In a television picture tube, electrons strike the screen after being accelerated from rest through a potential diff erence of 25 000 V. The speeds of the electrons are quite large, and for accurate calculations of the speeds, the eff ects of special relativity must be taken into account. Ignoring such eff ects, fi nd the electron speed just before the electron strikes the screen.

Multiple-Concept Example 4 deals with the concepts that are important in this problem. As illustrated in Figure 19.5b, a negatively charged particle is released from rest at point B and accelerates until it reaches point A. The mass and charge of the particle are 4.0 3 1026 kg and 22.0 3 1025 C, respectively. Only the gravitational force and the electrostatic force act on the particle, which moves on a horizontal straight line without rotating. The electric potential at A is 36 V greater than that at B; in other words, VA 2 VB 5 36 V. What is the translational speed of the particle at point A?

An electron and a proton, starting from rest, are accelerated through an electric potential diff erence of the same magnitude. In the process, the electron acquires a speed ve, while the proton acquires a speed vp. Find the ratio ve/vp.

The potential at location A is 452 V. A positively charged particle is released there from rest and arrives at location B with a speed vB. The potential at location C is 791 V, and when released from rest from this spot, the particle arrives at B with twice the speed it previously had, or 2vB. Find the potential at B.

A moving particle encounters an external electric fi eld that decreases its kinetic energy from 9520 eV to 7060 eV as the particle moves from position A to position B. The electric potential at A is 255.0 V, and the electric potential at B is 127.0 V. Determine the charge of the particle. Include the algebraic sign (1 or 2) with your answer.

During a lightning fl ash, there exists a potential diff erence of Vcloud 2 Vground 5 1.2 3 109 V between a cloud and the ground. As a result, a charge of 225 C is transferred from the ground to the cloud. (a) How much work Wgroundcloud is done on the charge by the electric force? (b) If the work done by the electric force were used to accelerate a 1100-kg automobile from rest, what would be its fi nal speed? (c) If the work done by the electric force were converted into heat, how many kilograms of water at 0 8C could be heated to 100 8C?

A particle is uncharged and is thrown vertically upward from ground level with a speed of 25.0 m/s. As a result, it attains a maximum height h. The particle is then given a positive charge 1q and reaches the same maximum height h when thrown vertically upward with a speed of 30.0 m/s. The electric potential at the height h exceeds the electric potential at ground level. Finally, the particle is given a negative charge 2q. Ignoring air resistance, determine the speed with which the negatively charged particle must be thrown vertically upward, so that it attains exactly the maximum height h. In all three situations, be sure to include the eff ect of gravity.

Two point charges, 13.40 mC and 26.10 mC, are separated by 1.20 m. What is the electric potential midway between them?

An electron and a proton are initially very far apart (eff ectively an infi nite distance apart). They are then brought together to form a hydrogen atom, in which the electron orbits the proton at an average distance of 5.29 3 10211 m. What is EPEfi nal 2 EPEinitial, which is the change in the electric potential energy?

Two charges A and B are fi xed in place, at diff erent distances from a certain spot. At this spot the potentials due to the two charges are equal. Charge A is 0.18 m from the spot, while charge B is 0.43 m from it. Find the ratio qB/qA of the charges

The drawing shows a square, each side of which has a length of L 5 0.25 m. On two corners of the square are fi xed diff erent positive charges, q1 and q2. Find the electric potential energy of a third charge q3 5 26.0 3 1029 C placed at corner A and then at corner B.

The drawing shows four point charges. The value of q is 2.0 mC, and the distance d is 0.96 m. Find the total potential at the location P. Assume that the potential of a point charge is zero at infi nity.

A charge of 1125 mC is fi xed at the center of a square that is 0.64 m on a side. How much work is done by the electric force as a charge of 17.0 mC is moved from one corner of the square to any other empty corner? Explain.

The drawing shows six point charges arranged in a rectangle. The value of q is 9.0 mC, and the distance d is 0.13 m. Find the total electric potential at location P, which is at the center of the rectangle.

Location A is 3.00 m to the right of a point charge q. Location B lies on the same line and is 4.00 m to the right of the charge. The potential diff erence between the two locations is VB 2 VA 5 45.0 V. What are the magnitude and sign of the charge?

Identical 11.8 mC charges are fi xed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fi xed to one of the empty corners, so that the total electric potential at the remaining empty corner is 0 V?

Charges of 2q and 12q are fi xed in place, with a distance of 2.00 m between them. A dashed line is drawn through the negative charge, perpendicular to the line between the charges. On the dashed line, at a distance L from the negative charge, there is at least one spot where the total potential is zero. Find L

Determine the electric potential energy for the array of three charges in the drawing, relative to its value when the charges are infi nitely far away and infi nitely far apart.

Two identical point charges (q 5 17.20 3 1026 C) are fi xed at diagonally opposite corners of a square with sides of length 0.480 m. A test charge (q0 5 22.40 3 1028 C), with a mass of 6.60 3 1028 kg, is released from rest at one of the empty corners of the square. Determine the speed of the test charge when it reaches the center of the square.

Two protons are moving directly toward one another. When they are very far apart, their initial speeds are 3.00 3 106 m/s. What is the distance of closest approach?

Four identical charges (12.0 mC each) are brought from infi nity and fi xed to a straight line. The charges are located 0.40 m apart. Determine the electric potential energy of this group.

A charge of 23.00 mC is fi xed in place. From a horizontal distance of 0.0450 m, a particle of mass 7.20 3 1023 kg and charge 28.00 mC is fi red with an initial speed of 65.0 m/s directly toward the fi xed charge. How far does the particle travel before its speed is zero?

Identical point charges of 11.7 mC are fi xed to diagonally opposite corners of a square. A third charge is then fi xed at the center of the square, such that it causes the potentials at the empty corners to change signs without changing magnitudes. Find the sign and magnitude of the third charge.

One particle has a mass of 3.00 3 1023 kg and a charge of 18.00 mC. A second particle has a mass of 6.00 3 1023 kg and the same charge. The two particles are initially held in place and then released. The particles fl y apart, and when the separation between them is 0.100 m, the speed of the 3.00 3 1023 kg particle is 125 m/s. Find the initial separation between the particles

Review Conceptual Example 7 as background for this problem. A positive charge 1q1 is located to the left of a negative charge 2q2. On a line passing through the two charges, there are two places where the total potential is zero. The fi rst place is between the charges and is 4.00 cm to the left of the negative charge. The second place is 7.00 cm to the right of the negative charge. (a) What is the distance between the charges? (b) Find uq1u/uq2u, the ratio of the magnitudes of the charges.

Two equipotential surfaces surround a 11.50 3 1028 C point charge. How far is the 190-V surface from the 75.0-V surface?

An equipotential surface that surrounds a point charge q has a potential of 490 V and an area of 1.1 m2 . Determine q.

The inner and outer surfaces of a cell membrane carry a negative and a positive charge, respectively. Because of these charges, a potential diff erence of about 0.070 V exists across the membrane. The thickness of the cell membrane is 8.0 3 1029 m. What is the magnitude of the electric fi eld in the membrane?

A positive point charge (q 5 17.2 3 1028 C) is surrounded by an equipotential surface A, which has a radius of rA 5 1.8 m. A positive test charge (q0 5 14.5 3 10211 C) moves from surface A to another equipotential surface B, which has a radius rB. The work done as the test charge moves from surface A to surface B is WAB 5 28.1 3 1029 J. Find rB.

A spark plug in an automobile engine consists of two metal conductors that are separated by a distance of 0.75 mm. When an electric spark jumps between them, the magnitude of the electric fi eld is 4.7 3 107 V/m. What is the magnitude of the potential diff erence DV between the conductors?

The drawing that accompanies Problem 60 shows a graph of a set of equipotential surfaces in cross section. The grid lines are 2.0 cm apart. Determine the magnitude and direction of the electric fi eld at position D. Specify whether the electric fi eld points toward the top or the bottom of the drawing.

An electric fi eld has a constant value of 4.0 3 103 V/m and is directed downward. The fi eld is the same everywhere. The potential at a point P within this region is 155 V. Find the potential at the following points: (a) 6.0 3 1023 m directly above P, (b) 3.0 3 1023 m directly below P, (c) 8.0 3 1023 m directly to the right of P.

An electron is released from rest at the negative plate of a parallel plate capacitor and accelerates to the positive plate (see the drawing). The plates are separated by a distance of 1.2 cm, and the electric fi eld within the capacitor has a magnitude of 2.1 3 106 V/m. What is the kinetic energy of the electron just as it reaches the positive plate?

he drawing shows the electric potential as a function of distance along the x axis. Determine the magnitude of the electric fi eld in the region (a) A to B, (b) B to C, and (c) C to D.

At a distance of 1.60 m from a point charge of 12.00 mC, there is an equipotential surface. At greater distances there are additional equipotential surfaces. The potential diff erence between any two successive surfaces is 1.00 3 103 V. Starting at a distance of 1.60 m and moving radially outward, how many of the additional equipotential surfaces are crossed by the time the electric fi eld has shrunk to one-half of its initial value? Do not include the starting surface.

The drawing shows a uniform electric fi eld that points in the negative y direction; the magnitude of the fi eld is 3600 N/C. Determine the electric potential diff erence (a) VB 2 VA between points A and B, (b) VC 2 VB between points B and C, and (c) VA 2 VC between points C and A.

What is the capacitance of a capacitor that stores 4.3 mC of charge on its plates when a voltage of 1.5 V is applied between them?

The electric potential energy stored in the capacitor of a defi brillator is 73 J, and the capacitance is 120 mF. What is the potential diff erence that exists across the capacitor plates?

Two identical capacitors store diff erent amounts of energy: capacitor A stores 3.1 3 1023 J, and capacitor B stores 3.4 3 1024 J. The voltage across the plates of capacitor B is 12 V. Find the voltage across the plates of capacitor A.

The electronic fl ash attachment for a camera contains a capacitor for storing the energy used to produce the fl ash. In one such unit, the potential diff erence between the plates of an 850-mF capacitor is 280 V. (a) Determine the energy that is used to produce the fl ash in this unit. (b) Assuming that the fl ash lasts for 3.9 3 1023 s, fi nd the eff ective power or wattage of the fl ash.

The same voltage is applied between the plates of two diff erent capacitors. When used with capacitor A, this voltage causes the capacitor to store 11 mC of charge and 5.0 3 1025 J of energy. When used with capacitor B, which has a capacitance of 6.7 mF, this voltage causes the capacitor to store a charge that has a magnitude of qB. Determine qB.

A parallel plate capacitor has a capacitance of 7.0 mF when fi lled with a dielectric. The area of each plate is 1.5 m2 and the separation between the plates is 1.0 3 1025 m. What is the dielectric constant of the dielectric?

Two capacitors are identical, except that one is empty and the other is fi lled with a dielectric (k 5 4.50). The empty capacitor is connected to a 12.0-V battery. What must be the potential diff erence across the plates of the capacitor fi lled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

The membrane that surrounds a certain type of living cell has a surface area of 5.0 3 1029 m2 and a thickness of 1.0 3 1028 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.0. (a) The potential on the outer surface of the membrane is 160.0 mV greater than that on the inside surface. How much charge resides on the outer surface? (b) If the charge in part (a) is due to positive ions (charge 1e), how many such ions are present on the outer surface?

Capacitor A and capacitor B both have the same voltage across their plates. However, the energy of capacitor A can melt m kilograms of ice at 0 8C, while the energy of capacitor B can boil away the same amount of water at 100 8C. The capacitance of capacitor A is 9.3 mF. What is the capacitance of capacitor B?

What is the potential diff erence between the plates of a 3.3-F capacitor that stores suffi cient energy to operate a 75-W light bulb for one minute?

A capacitor is constructed of two concentric conducting cylindrical shells. The radius of the inner cylindrical shell is 2.35 3 1023 m, and that of the outer shell is 2.50 3 1023 m. When the cylinders carry equal and opposite charges of magnitude 1.7 3 10210 C, the electric fi eld between the plates has an average magnitude of 4.2 3 104 V/m and is directed radially outward from the inner shell to the outer shell. Determine (a) the magnitude of the potential diff erence between the cylindrical shells and (b) the capacitance of this capacitor.

Review Conceptual Example 10 before attempting this problem. An empty capacitor is connected to a 12.0-V battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material (k 5 2.8) is inserted between the plates. Find the amount by which the potential diff erence across the plates changes. Specify whether the change is an increase or a decrease.

An empty parallel plate capacitor is connected between the terminals of a 9.0-V battery and charged up. The capacitor is then disconnected from the battery, and the spacing between the capacitor plates is doubled. As a result of this change, what is the new voltage between the plates of the capacitor?

The potential diff erence between the plates of a capacitor is 175 V. Midway between the plates, a proton and an electron are released. The electron is released from rest. The proton is projected perpendicularly toward the negative plate with an initial speed. The proton strikes the negative plate at the same instant that the electron strikes the positive plate. Ignore the attraction between the two particles, and fi nd the initial speed of the proton.

If the electric fi eld inside a capacitor exceeds the dielectric strength of the dielectric between its plates, the dielectric will break down, discharging and ruining the capacitor. Thus, the dielectric strength is the maximum magnitude that the electric fi eld can have without breakdown occurring. The dielectric strength of air is 3.0 3 106 V/m, and that of neoprene rubber is 1.2 3 107 V/m. A certain air-gap, parallel plate capacitor can store no more than 0.075 J of electrical energy before breaking down. How much energy can this capacitor store without breaking down after the gap between its plates is fi lled with neoprene rubber?

An axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant 5 5, thickness 5 1 3 1028 m) is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. Assuming that the membrane acts like a parallel plate capacitor with a plate area of 5 3 1026 m2 , what is its capacitance?

Refer to Multiple-Concept Example 3 to review the concepts that are needed here. A cordless electric shaver uses energy at a rate of 4.0 W from a rechargeable 1.5-V battery. Each of the charged particles that the battery delivers to the shaver carries a charge that has a magnitude of 1.6 3 10219 C. A fully charged battery allows the shaver to be used for its maximum operation time, during which 3.0 3 1022 of the charged particles pass between the terminals of the battery as the shaver operates. What is the shavers maximum operation time?

Point A is located 0.25 m away from a charge of 22.1 3 1029 C. Point B is located 0.50 m away from the charge. What is the electric potential diff erence VB 2 VA between these two points?

The drawing shows a graph of a set of equipotential surfaces seen in cross section. Each is labeled according to its electric potential. A 12.8 3 1027 C point charge is placed at position A. Find the work that is done on the point charge by the electric force when it is moved (a) from A to B, and (b) from A to C

The work done by an electric force in moving a charge from point A to point B is 2.70 3 1023 J. The electric potential diff erence between the two points is VA 2 VB 5 50.0 V. What is the charge?

Two capacitors have the same plate separation, but one has square plates and the other has circular plates. The square plates are a length L on each side, and the diameter of the circular plate is L. The capacitors have the same capacitance because they contain diff erent dielectric materials. The dielectric constant of the material between the square plates has a value of ksquare 5 3.00. What is the dielectric constant kcircle of the material between the circular plates?

Three point charges, 25.8 3 1029 C, 29.0 3 1029 C, and 17.3 3 1029 C, are fi xed at diff erent positions on a circle. The total electric potential at the center of the circle is 22100 V. What is the radius of the circle?

Equipotential surface A has a potential of 5650 V, while equipotential surface B has a potential of 7850 V. A particle has a mass of 5.00 3 1022 kg and a charge of 14.00 3 1025 C. The particle has a speed of 2.00 m/s on surface A. A nonconservative outside force is applied to the particle, and it moves to surface B, arriving there with a speed of 3.00 m/s. How much work is done by the outside force in moving the particle from A to B?

An empty capacitor has a capacitance of 3.2 mF and is connected to a 12-V battery. A dielectric material (k 5 4.5) is inserted between the plates of this capacitor. What is the magnitude of the surface charge on the dielectric that is adjacent to either plate of the capacitor? (Hint: The surface charge is equal to the diff erence in the charge on the plates with and without the dielectric.)

A positive charge q1 is located 3.00 m to the left of a negative charge q2. The charges have diff erent magnitudes. On the line through the charges, the net electric fi eld is zero at a spot 1.00 m to the right of the negative charge. On this line there are also two spots where the total electric potential is zero. Locate these two spots relative to the negative charge.

The drawing shows a parallel plate capacitor. One-half of the region between the plates is fi lled with a material that has a dielectric constant k1. The other half is fi lled with a material that has a dielectric constant k2. The area of each plate is A, and the plate separation is d. The potential diff erence across the plates is V. Note especially that the charge stored by the capacitor is q1 1 q2 5 CV, where q1 and q2 are the charges on the area of the plates in contact with materials 1 and 2, respectively. Show that C 5 P0A(k1 1 k2)/(2d).

Two particles each have a mass of 6.0 3 1023 kg. One has a charge of 15.0 3 1026 C, and the other has a charge of 25.0 3 1026 C. They are initially held at rest at a distance of 0.80 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-third its initial value?

The capacitance of an empty capacitor is 1.2 mF. The capacitor is connected to a 12-V battery and charged up. With the capacitor connected to the battery, a slab of dielectric material is inserted between the plates. As a result, 2.6 3 1025 C of additional charge fl ows from one plate, through the battery, and onto the other plate. What is the dielectric constant of the material?

Particle 1 has a mass of m1 5 3.6 3 1026 kg, while particle 2 has a mass of m2 5 6.2 3 1026 kg. Each has the same electric charge. These particles are initially held at rest, and the two-particle system has an initial electric potential energy of 0.150 J. Suddenly, the particles are released and fl y apart because of the repulsive electric force that acts * on each one (see the fi gure). The eff ects of the gravitational force are negligible, and no other forces act on the particles. Concepts: (i) What types of energy does the two-particle system have initially? (ii) What types of energy does the two-particle system have at the instant illustrated in part b of the drawing? (iii) Does the principle of conservation of energy apply to this problem? Explain. (iv) Does the conservation of linear momentum apply to the two particles as they fl y apart? Explain. Calculations: At one instant following the release, the speed of particle 1 is measured to be v1 5 170 m/s. What is the electric potential energy at this instant?

Two identical point charges (12.4 3 1029 C) are fi xed in place, separated by 0.50 m (see the fi gure). Concepts: (i) The electric fi eld is a vector and has a direction. At the midpoint, what are the directions of the individual electric-fi eld contributions from qA and qB? (ii) Is the magnitude of the net electric fi eld at the midpoint greater than, less than, or equal to zero? (iii) Is the total electric potential at the midpoint positive, negative, or zero? (iv) Does the electric potential have a direction associated with it? Explain. Calculations: Find the electric fi eld and the electric potential at the midpoint of the line between the charges qA and qB..