Question: A potential difference of 90.0 mV

> Metal sphere A of radius 12.0 cm carries 6.00 μC of charge, and metal sphere B of radius 18.0 cm carries -4.00 μC of charge. If the two spheres are attached by a very long conducting thread, what is the final distribution of charge on the two spheres?

> Two positive charges each of charge q are fixed on the y - axis, one at y = d and the other at y = -d as in Figure P16.70. A third positive charge 2q located on the x - axis at x = 2d is released from rest. Find symbolic expressions for (a) The total ele

> Oppositely charged parallel plates are separated by 5.33 mm. A potential difference of 600. V exists between the plates. (a) What is the magnitude of the electric field between the plates? (b) What is the magnitude of the force on an electron between the

> Capacitors C1 = 6.0 μF and C2 = 2.0 μF are charged as a parallel combination across a 250 - V battery. The capacitors are disconnected from the battery and from each other. They are then connected positive plate to negative plate and negative plate to po

> When a certain air - filled parallel - plate capacitor is connected across a battery, it acquires a charge of 150. μC on each plate. While the battery connection is maintained, a dielectric slab is inserted into, and fills, the region between the plates.

> The immediate cause of many deaths is ventricular fibrillation, an uncoordinated quivering of the heart, as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes

> A spherical capacitor consists of a spherical conducting shell of radius b and charge -Q concentric with a smaller conducting sphere of radius a and charge Q. (a) Find the capacitance of this device. (b) Show that as the radius b of the outer sphere appr

> An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 400-g sample of silver at an initial temperature of 87°C is placed in the water. The stirrer is used to stir the mixture until it reaches its final equilibrium temperature

> Find the equivalent capacitance of the group of capacitors shown in Figure P16.65. Figure P16.65:

> Two charges of 1.0 μC and -2.0 μC are 0.50 m apart at two vertices of an equilateral triangle as in Figure P16.64. (a) What is the electric potential due to the 1.0-μC charge at the third vertex, point P? (b) Wha

> A parallel-plate capacitor is constructed using a dielectric material whose dielectric constant is 3.00 and whose dielectric strength is 2.00 x 108 V/m. The desired capacitance is 0.250 μF, and the capacitor must withstand a maximum potential difference

> Two capacitors give an equivalent capacitance of Cp when connected in parallel and an equivalent capacitance of Cs when connected in series. What is the capacitance of each capacitor?

> A parallel-plate capacitor with a plate separation d has a capacitance C0 in the absence of a dielectric. A slab of dielectric material of dielectric constant k and thickness d/3 is then inserted between the plates as in Figure P16.61a. Show that the cap

> For the system of four capacitors shown in Figure P16.41, find (a) The total energy stored in the system and (b) The energy stored by each capacitor. (c) Compare the sum of the answers in part (b) with your result to part (a) and explain your observation

> Three parallel-plate capacitors are constructed, each having the same plate area A and with C1 having plate spacing d1, C2 having plate spacing d2, and C3 having plate spacing d3. Show that the total capacitance C of the three capacitors connected in ser

> When a potential difference of 150. V is applied to the plates of an air-filled parallel-plate capacitor, the plates carry a surface charge density of 3.00 x 10-10 C/cm2. What is the spacing between the plates?

> A model of a red blood cell portrays the cell as a spherical capacitor, a positively charged liquid sphere of surface area A separated from the surrounding negatively charged fluid by a membrane of thickness t. Tiny electrodes introduced into the interio

> Lead pellets, each of mass 1.00 g, are heated to 200.°C. How many pellets must be added to 0.500 kg of water that is initially at 20.0°C to make the equilibrium temperature 25.0°C? Neglect any energy transfer to or from the container.

> A parallel-plate capacitor has plates of area A = 7.00 x 10-2 m2 separated by distance d = 2.00 x 10-4 m. (a) Calculate the capacitance if the space between the plates is filled with air. What is the capacitance if the space is filled half with air and h

> Determine (a) The capacitance and (b) The maximum voltage that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 175 cm2 and an insulation thickness of 0.0400 mm.

> (a) How much charge can be placed on a capacitor with air between the plates before it breaks down if the area of each plate is 5.00 cm2? (b) Find the maximum charge if polystyrene is used between the plates instead of air. Assume the dielectric strength

> The voltage across an air-filled parallel-plate capacitor is measured to be 85.0 V. When a dielectric is inserted and completely fills the space between the plates as in Figure P16.53, the voltage drops to 25.0 V. (a) What is the dielectric constant of t

> Each plate of a 5.00 μF capacitor stores 60.0 μC of charge. (a) Find the potential difference across the plates. (b) How much energy is stored in the capacitor?

> A parallel-plate capacitor has capacitance 3.00 μF. (a) How much energy is stored in the capacitor if it is connected to a 6.00-V battery? (b) If the battery is disconnected and the distance between the charged plates doubled, what is the energy stored?

> Two capacitors, C1 = 18.0 μF and C2 = 36.0 μF, are connected in series, and a 12.0-V battery is connected across them. (a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor. (b) Find the energy stored in each individu

> A constant electric field accelerates a proton from rest through a distance of 2.00 m to a speed of 1.50 x 105 m/s. (a) Find the change in the proton’s kinetic energy. (b) Find the change in the system’s electric potential energy. (c) Calculate the magni

> A 12.0-V battery is connected to a 4.50-μF capacitor. How much energy is stored in the capacitor?

> Four capacitors are connected as shown in Figure P16.48. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor, taking ΔVab = 15.0 V. Figure P16.48:

> What mass of water at 25.0°C must be allowed to come to thermal equilibrium with a 1.85-kg cube of aluminum initially at 1.50 x 102°C to lower the temperature of the aluminum to 65.0°C? Assume any water turned to steam subsequently recondenses.

> A 1.00-μF capacitor is charged by being connected across a 10.0-V battery. It is then disconnected from the battery and connected across an un-charged 2.00-μF capacitor. Determine the resulting charge on each capacitor.

> (a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P16.46 if C1 = 5.00 μF, C2 = 10.00 μF, and C3 = 2.00 μF. (b) If the potential between points a a

> A 25.0-μF capacitor and a 40.0-μF capacitor are charged by being connected across separate 50.0-V batteries. (a) Determine the resulting charge on each capacitor. (b) The capacitors are then disconnected from their batteries and connected to each other,

> Three capacitors are connected to a battery as shown in Figure P16.44. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C. (a) What is the equivalent capacitance of this set of capacitors? (b) State the ranking of the capacitors according to the charge

> Find the charge on each of the capacitors in Figure P16.43. Figure P16.43:

> Consider the combination of capacitors in Figure P16.42. (a) Find the equivalent single capacitance of the two capacitors in series and redraw the diagram (called diagram 1) with this equivalent capacitance. (b) In diagram 1, find the equivalent capacita

> For the system of capacitors shown in Figure P16.41, find (a) The equivalent capacitance of the system, (b) The charge on each capacitor, and (c) The potential difference across each capacitor. Figure P16.41:

> Two capacitors give an equivalent capacitance of 9.00 pF when connected in parallel and an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor?

> Cathode ray tubes (CRTs) used in old-style televisions have been replaced by modern LCD and LED screens. Part of the CRT included a set of accelerating plates separated by a distance of about 1.50 cm. If the potential difference across the plates was 25.

> Find (a) The equivalent capacitance of the capacitors in Figure P16.39, (b) The charge on each capacitor, and (c) The potential difference across each capacitor. Figure P16.39:

> In the summer of 1958 in St. Petersburg, Florida, a new sidewalk was poured near the childhood home of one of the authors. No expansion joints were supplied, and by mid- July, the sidewalk had been completely destroyed by thermal expansion and had to be

> Two capacitors, C1 = 5.00 μF and C2 = 12.0 μF, are connected in parallel, and the resulting combination is connected to a 9.00-V battery. Find (a) The equivalent capacitance of the combination, (b) The potential difference across each capacitor, and (c)

> Given a 2.50-μF capacitor, a 6.25-μF capacitor, and a 6.00-V battery, find the charge on each capacitor if you connect them (a) In series across the battery and (b) In parallel across the battery.

> A small object with a mass of 350. μg carries a charge of 30.0 nC and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plates are separated by 4.00 cm. If the thread makes an angle of 15.08 with the vertical, what i

> A parallel-plate capacitor with area 0.200 m2 and plate separation of 3.00 mm is connected to a 6.00-V battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric field between the plates? (d) Find the magn

> A 1-megabit computer memory chip contains many 60.0 x 10-15-F capacitors. Each capacitor has a plate area of 21.0 x 10-12 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration.) The diameter of an atom is on the o

> An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2 and separated by a distance of 1.80 mm. If a 20.0-V potential difference is applied to these plates, calculate (a) The electric field between the plates, (b) The capac

> Air breaks down and conducts charge as a spark if the electric field magnitude exceeds 3.00 x 106 V/m. (a) Determine the maximum charge Qmax that can be stored on an air-filled parallel-plate capacitor with a plate area of 2.00 x 10-4 m2. (b) A 75.0 μF a

> An air-filled parallel-plate capacitor has plates of area 2.30 cm2 separated by 1.50 mm. The capacitor is connected to a 12.0-V battery. (a) Find the value of its capacitance. (b) What is the charge on the capacitor? (c) What is the magnitude of the unif

> (a) When a 9.00-V battery is connected to the plates of a capacitor, it stores a charge of 27.0 μC. What is the value of the capacitance? (b) If the same capacitor is connected to a 12.0-V battery, what charge is stored?

> A swimming pool filled with water has dimensions of 5.00 m x 10.0 m x 1.78 m. (a) Find the mass of water in the pool. (b) Find the thermal energy required to heat the pool water from 15.5°C to 26.5°C. (c) Calculate the cost of heating the pool from 15.5°

> Consider the Earth and a cloud layer 8.0 x 102 m above the planet to be the plates of a parallel-plate capacitor. (a) If the cloud layer has an area of 1.0 km2 = 1.0 x 106 m2, what is the capacitance? (b) If an electric field strength greater than 3.0 x

> In the classical model of a hydrogen atom, an electron orbits a proton with a kinetic energy of +13.6 eV and an electric potential energy of -27.2 eV. (a) Use the kinetic energy to calculate the classical orbital speed. (b) Use the electric potential ene

> An alpha particle, which has charge 3.20 x 10-19 C, is moved from point A, where the electric potential is 3.60 x 103 J/C, to point B, where the electric potential is 5.80 x 103 J/C. Calculate the work done by the electric field on the alpha particle in

> An electric field does 1.50 x 103 eV of work on a carbon nucleus of charge 9.61 x 10-19 C. Find the change in the nucleus’ (a) Electric potential and (b) Electric potential energy in joules.

> Calculate the speed of (a) An electron and (b) A proton with a kinetic energy of 1.00 electron volt (eV). (c) Calculate the average translational kinetic energy in eV of a 3.00 x 102-K ideal gas particle.

> Four point charges each having charge Q are located at the corners of a square having sides of length a. Find symbolic expressions for (a) The total electric potential at the center of the square due to the four charges and (b) The work required to bring

> In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 x 10-27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initi

> The metal sphere of a small Van de Graaff generator illustrated in Figure 15.23 has a radius of 18 cm. When the electric field at the surface of the sphere reaches 3.0 x 106 V/m, the air breaks down, and the generator discharges. What is the maximum pote

> A tiny sphere of mass 8.00 μg and charge -2.80 nC is initially at a distance of 1.60 μm from a fixed charge of +8.50 nC. If the 8.00 - mg sphere is released from rest, find (a) Its kinetic energy when it is 0.500 μm from the fixed charge and (b) Its spee

> A proton and an alpha particle (charge = 2e, mass = 6.64 x 10-27 kg) are initially at rest, separated by 4.00 x 10-15 m. (a) If they are both released simultaneously, explain why you can’t find their velocities at infinity using only conservation of ener

> A 1.5-kg copper block is given an initial speed of 3.0 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest. (a) If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in tempe

> A proton is released from rest in a uniform electric field of magnitude 385 N/C. Find (a) The electric force on the proton, (b) The acceleration of the proton, and (c) The distance it travels in 2.00 μs.

> A proton is located at the origin, and a second proton is located on the x - axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 x 10-27 kg)

> A positive point charge q = +2.50 nC is located at x = 1.20 m and a negative charge of -2q = -5.00 nC is located at the origin as in Figure P16.18. (a) Sketch the electric potential versus x for points along the x - axis in the range -1.50 m (b) Find a s

> The three charges in Figure P16.17 are at the vertices of an isosceles triangle. Let q = 7.00 nC and calculate the electric potential at the midpoint of the base. Figure P16.17:

> Three identical point charges each of charge q are located at the vertices of an equilateral triangle as in Figure P16.16. The distance from the center of the triangle to each vertex is a. (a) Show that the electric field at the center of the triangle is

> Two point charges Q1 = +5.00 nC and Q2 = -3.00 nC are separated by 35.0 cm. (a) What is the electric potential at a point midway between the charges? (b) What is the potential energy of the pair of charges? What is the significance of the algebraic sign

> Three charges are situated at corners of a rectangle as in Figure P16.13. How much work must an external agent do to move the 8.00-μC charge to infinity? Figure P16.13:

> (a) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in Figure P16.13. (b) Repeat if the 2.00-μC charge is replaced with a charge of -2.00 μC. Figu

> The two charges in Figure P16.12 are separated by d = 2.00 cm. Find the electric potential at (a) point A and (b) point B, which is halfway between the charges. Figure P16.12:

> An electron is at the origin. (a) Calculate the electric potential VA at point A, x = 0.250 cm. (b) Calculate the electric potential VB at point B, x = 0.750 cm. What is the potential difference VB - VA? (c) Would a negatively charged particle placed at

> A 0.200-kg aluminum cup contains 800. g of water in thermal equilibrium with the cup at 80.°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.5°C per minute. At what rate is energy being removed? Express your

> On planet Tehar, the free-fall acceleration is the same as that on the Earth, but there is also a strong downward electric field that is uniform close to the planet’s surface. A 2.00-kg ball having a charge of 5.00 μC is thrown upward at a speed of 20.1

> A uniform electric field of magnitude 375 N/C pointing in the positive x - direction acts on an electron, which is initially at rest. After the electron has moved 3.20 cm, what is (a) The work done by the field on the electron, (b) The change in potentia

> Two small identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of 12 x 10-9 C, the other a charge of -18 x 10-9 C. (a) Find the electrostatic force exerted on one sphere by the other. (b) The spheres are connecte

> Four point charges are at the corners of a square of side a as shown in Figure P15.8. Determine the magnitude and direction of the resultant electric force on q, with ke, q, and a left in symbolic form. Figure P15.8:

> Protons are projected with an initial speed v0 = 9550 m/s into a region where a uniform electric field of magnitude E = 720 N/C is present (Fig. P15.70). The protons are to hit a target that lies a horizontal distance of 1.27 mm from the point where the

> Two uncharged spheres are separated by 2.00 m. If 3.50 x 1012 electrons are removed from one sphere and placed on the other, determine the magnitude of the Coulomb force on one of the spheres, treating the spheres as point charges.

> Each of the electrons in a particle beam has a kinetic energy of 1.60 x 10-17 J. (a) What is the magnitude of the uniform electric field (pointing in the direction of the electrons’ movement) that will stop these electrons in a distance of 10.0 cm? (b) H

> Three identical point charges, each of mass m = 0.100 kg, hang from three strings, as shown in Figure P15.68. If the lengths of the left and right strings are each L = 30.0 cm and if the angle θ is 45.0°, determine the value of q.

> A solid conducting sphere of radius 2.00 cm has a charge of 8.00 μC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge of -4.00 μC. Find the electric field at (a) r = 1.00 c

> Two small beads having positive charges q1 = 3q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q1 is at the origin. As shown in Figure P15.66, a third small charged bead is free to slid

> The apparatus shown in Figure P11.12 was used by Joule to measure the mechanical equivalent of heat. Work is done on the water by a rotating paddle wheel, which is driven by two blocks falling at a constant speed. The temperature of the stirred water inc

> Rank the potential energies of the four systems of particles shown in Figure CQ16.4 from largest to smallest. Include equalities if appropriate. Figure CQ16.4:

> Two hard rubber spheres, each of mass m = 15.0 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 5.00 cm whose support points are a distance d = 3.00 cm from each other as shown in Figure P15.65. During

> A point charge of magnitude 5.00 μC is at the origin of a coordinate system, and a charge of -4.00 μC is at the point x = 1.00 m. There is a point on the x - axis, at x less than infinity, where the electric field goes to zero. (a) Show by conceptual arg

> Two 2.0- g spheres are suspended by 10.0 - cm - long light strings (Fig. P15.63). A uniform electric field is applied in the x - direction. If the spheres have charges of -5.0 x 10-8 C and +5.0 x 10-8 C, determine the electric field intensity that enable

> A 1.00 - g cork ball having a positive charge of 2.00 mC is suspended vertically on a 0.500 - m - long light string in the presence of a uniform downward - directed electric field of magnitude E = 1.00 x 105 N/C as in Figure P15.62. If the ball is displa

> A point charge +2Q is at the origin and a point charge -Q is located along the x - axis at x = d as in Figure P15.61. Find symbolic expressions for the components of the net force on a third point charge +Q located along the y - axis at y = d. Figure P1

> The electrons in a particle beam each have a kinetic energy K. Find the magnitude of the electric field that will stop these electrons in a distance d, expressing the answer symbolically in terms of K, e, and d. Should the electric field point in the dir

> A molecule of DNA (deoxyribonucleic acid) is 2.17 mm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.00% upon becoming charged. Determine the effec

> A proton moving at v0 = 1.50 x 106 m/s enters the region between two parallel plates with charge densities of magnitude σ = 4.20 x 10-9 C/m2 (Fig. P15.59). Calculate (a) The magnitude of the electric field between the plates, and (b) The magni

> A small plastic ball of mass m = 2.00 g is suspended by a string of length L = 20.0 cm in a uniform electric field, as shown in Figure P15.58. If the ball is in equilibrium when the string makes a θ = 15.0° angle with the vertical

> Three point charges are aligned along the x - axis as shown in Figure P15.57. Find the electric field at the position x = 12.0 m, y = 0. Figure P15.57:

> A 5.00-g lead bullet traveling at 3.00 x 102 m/s is stopped by a large tree. If half the kinetic energy of the bullet is transformed into internal energy and remains with the bullet while the other half is transmitted to the tree, what is the increase in

> A non-conducting, thin plane sheet of charge carries a uniform charge per unit area of 5.20 μC/m2 as in Figure 15.30. (a) Find the electric field at a distance of 8.70 cm from the plate. (b) Explain whether your result changes as the distan

> In deep space, two spheres each of radius 5.00 m are connected by a 3.00 x 102 m non-conducting cord. If a uniformly distributed charge of 35.0 mC resides on the surface of each sphere, calculate the tension in the cord.

> A very large non-conducting plate lying in the xy - plane carries a charge per unit area of σ. A second such plate located at z = 2.00 cm and oriented parallel to the xy - plane carries a charge per unit area of -2σ. Find the electric field (a) For z < 0

> Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m, find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m.

> A charge of 1.70 x 102 μC is at the center of a cube of edge 80.0 cm. No other charges are nearby. (a) Find the flux through the whole surface of the cube. (b) Find the flux through each face of the cube. (c) Would your answers to parts (a) or (b) change