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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Exercise 23.43 shows that, outside a spherical shell with uniform surface charge, the potential is the same as if all the charge were concentrated into a point charge at the center of the sphere. (a)
Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. One sphere is 60.0 cm in diameter, has mass 50.0 g and
Use the electric field calculated in Problem 22.43 to calculate the potential difference between the solid conducting sphere and the thin insulating shell.
Consider a solid conducting sphere inside a hollow conducting sphere, with radii and charges specified in Problem 22.42. Take V = 0 as r→ ∞. Use the electric field calculated in Problem
Electric charge is distributed uniformly along a thin rod of length a, with total charge Q. Take the potential to be zero at infinity Find the potential at the following points (Fig)(a) point P, a
(a) If a spherical raindrop of radius 0.650 mm carries a charge of -1.20 µC uniformly distributed over its volume, what is the potential at its surface? (Take the potential to be zero at an infinite
1\\'0 metal spheres of different sizes are charged such that the electric potential is the same at the surface of each. Sphere A has a radius three times that of sphere B. Let QA and QB be the
An alpha particle with kinetic energy 11.0 MeV makes a head-on collision with a lead nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the lead nucleus
A metal sphere with radius R1 has a charge Q1. Take the electric potential to be zero at an infinite distance from the sphere. (a) What are the electric field and electric potential at the surface of
Use the charge distribution and electric field calculated in Problem 22.57. (a) Show that for r ≥ R the potential is identical to that produced by a point charge Q. (Take the potential to be
Nuclear Fusion in the Sun The source of the sun's energy is a sequence of nuclear reactions that occur in its core. The first of these reactions involves the collision of two protons, which fuse
V(x, y, z) = A(x2 - 3y2 + Z2)Where A is a constant(a) Derive an expression for the electric field E at any point in this region. (b) The work done by the field when a 1.50-µC test charge moves from
Nuclear Fission The unstable nucleus of uranium- 236 can be regarded as a uniformly charged sphere of charge Q = +92e and radius R = 7.4 X 10-l5 m. In nuclear fission, this can divide into two
In a certain region, a charge distribution exists that is spherically symmetric but nonuniform. That is, the volume charge density p(r) depends on the distance r from the center of the distribution
In experiments in which atomic nuclei collide, head-on collisions like that described in Problem 23.82 do happen, but “near misses” are more common. Suppose the alpha particle in Problem 23.82
A hollow, thin-walled insulating cylinder of radius R and length L (like the cardboard tube in a roll of toilet paper) bas charge Q uniformly distributed over its surface. (a) Calculate the electric
The Millikan Oil-Drop Experiment The charge of an electron was first measured by the American physicist Robert Millikan during 1909-1913. In his experiment, oil is sprayed in very fine drops (around
Two point charges are moving to the right along the x-axis. Point charge 1 has charge ql = 2.00 µC mass ml = 6.00 X 10-5 kg, and speed u1 Point charge 2 is to the right of ql and has charge q2
A capacitor has a capacitance of 7.28 µF. What amount of charge must be placed on each of its plates to make the potential difference between its plates equal to 25.0 V?
The plates of a parallel-plate capacitor are 3.28 mm apart, and each has an area of 12.2 cm2. Each plate carries a charge of magnitude 4.35 X 10-8 C. The plates are in vacuum. (a) What is the
A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 µC on each plate. The plates are 0.328 mm apart. (a) What is the potential difference between the plates? (b)
Capacitance of an Oscilloscope Oscilloscopes has parallel metal plates inside them to deflect the electron beam. These plates are called the deflecting plates. Typically, they are squares 3.0 cm on a
A 10.0-µF parallel-plate capacitor with circular plates is connected to a 12.0-V battery. (a) What is the charge on each plate? (b) How much charge would be on the plates if their separation were
A 10.0-µF parallel-plate capacitor is connected to a 12.0-V battery. After the capacitor is fully charged, the battery is disconnected without loss of any of the charge on the plates. (a) A
How far apart would parallel pennies have to be to make a 1.00-pF capacitor? Does your answer suggest that you are justified in treating these pennies as infinite sheets? Explain.
A 5.00-pF, parallel-plate, air-filled capacitor with circular plates is to be used in a circuit in which it will be subjected to potentials of up to 1.00 X 102 V. The electric field between the
A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each
A cylindrical capacitor consists of a solid inner conducting core with radius 0.250 cm, surrounded by an outer hollow conducting tube. The two conductors are separated by air, and the length of the
A cylindrical capacitor has an inner conductor of radius 1.5 mm and an outer conductor of radius 3.5 mm. The two conductors are separated by vacuum, and the entire capacitor is 2.8 m long. (a) What
A spherical capacitor is formed from two concentric, spherical, conducting shells separated by vacuum. The inner sphere has radius 15.0 cm and the capacitance is 116 pF. (a) What is the radius of the
A spherical capacitor contains a charge of 3.30 nC when connected to a potential difference of 220 V. If its plates are separated by vacuum and the inner radius of the outer shell is 4.00 cm,
For the system of capacitors shown in Fig. 24.24, find the equivalent capacitance(a) Between b and c, and(b) Between a and c.
In Fig. each capacitor has C = 4.00 µF and Vab = +28.0 V. Calculate(a) The charge on each capacitor;(b) The potential difference across each capacitor;(c) The potential difference between
In Fig. let C1 = 3.00µF, C2 = 5.00µF, and Vab = +52.0 V. Calculate(a) The charge on each capacitor and(b) The potential difference across each capacitor.
In Fig, let C1 = 3.00µF. C2 = 5.00µF. and Vab = +52.0 V. Calculate (a) The charge on each capacitor and (b) The potential difference across each capacitor
In Fig, C1 = 6.00µF, C2 = 3.00µF, and C3 = 5.00µF. The capacitor network is connected to an applied potential Vab. After the charges on the capacitors have reached their final
In Fig. C1 = 3.00µF and Vab = 120 V. The charge on capacitor C1 is 150 µC. Calculate the voltage across the other two capacitors.
Two parallel-plate vacuum capacitors have plate spacings d1 and d2 and equal plate areas A. Show that when the capacitors are connected in series, the equivalent capacitance is the same as for a
Two parallel-plate vacuum capacitors have areas A1 and A2 and equal plate spacings d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single
Figure shows a system of four capacitors, where the potential difference across ab is 50.0V.(a) Find the equivalent capacitance of this system between a and b.(b) How much charge is stored by this
Suppose the 3-µF capacitor in Fig. were removed and replaced by a different one, and that this changed the equivalent capacitance between points a and b to 8µF. What would be the capacitance of the
A parallel-plate air capacitor has a capacitance of 920 pF. The charge on each plate is 2.55µC. (a) What is the potential difference between the plates? (b) If the charge is kept constant, what will
A 5.80-µF, parallel-plate, air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in units
An air capacitor is made from two flat parallel plates 1.50 mm apart. The magnitude of charge on each plate is 0.0180µC when the potential difference is 200 V. (a) What is the capacitance? (b) What
A 450-µF capacitor is charged to 295 V. Then a wire is connected between the plates. How many joules of thermal energy are produced as the capacitor discharges if all of the energy that was stored
A capacitor of capacitance C is charged to a potential difference V0. The terminals of the charged capacitor are then connected to those of an uncharged capacitor of capacitance C/2 Compute (a) The
A parallel-plate vacuum capacitor with plate area A and separation x has charges + Q and - Q on its plates. The capacitor is disconnected from the source of charge, so the charge on each plate
A parallel-plate vacuum capacitor with plate area A and separation x has charges + Q and - Q on its plates. The capacitor is disconnected from the source of charge, so the charge on each plate
(a) How much charge does a battery have to supply to a 5.0-µF capacitor to create a potential difference of 1.5 V across its plates? How much energy is stored in the capacitor in this case? (b) How
For the capacitor network shown in Fig, the potential difference across ab is 36 V. Find(a) The total charge stored in this network;(b) The charge on each capacitor;(c) The total energy stored in the
For the capacitor net- work shown in Fig. the potential difference across ab is 220 V Find(a) The total charge stored in this network;(b) The charge on each capacitor;(c) The total energy stored in
A 0.350-m-long cylindrical capacitor consists of a solid conducting core with a radius of 1.20 mm and an outer hollow conducting tube with an inner radius of2.00 mm. The two conductors are separated
A cylindrical air capacitor of length 15.0 m stores 3.20 X 10-9 J of energy when the potential difference between the two conductors is 4.00 V. (a) Calculate the magnitude of the charge on each
A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm, and the outer sphere has radius 14.8 cm. A potential difference of 120
You have two identical capacitors and an external potential source. (a) Compare the total energy stored in the capacitors when they are connected to the applied potential in series and in parallel.
A parallel-plate capacitor has capacitance Co = 5.00 pF when there is air between the plates. The separation between the plates is l.50 mm. (a) What is the maximum magnitude of charge Q that can be
Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is E = 3.20 X 105 v/m. When the space is filled with dielectric, the electric
A budding electronics hobbyist wants to make a simple 1.0-nF capacitor for tuning her crystal radio, using two sheets of aluminum foil as plates, with a few sheets of paper between them as a
The dielectric to be used in a paral1el-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60 X 107 V/m. The capacitor is to have a capacitance of 1.25 X 10- 9 F and
Show that Eq. (24.20) holds for a paral1el-plate Capacitor with a dielectric material between the plates. Use a derivation analogous to that used for Eq. (24.11).
A capacitor has parallel plates of area 12 cm' separated by 2.0 mm. The space between the plates is filled with polystyrene (see Table 24.2). (a) Find the permittivity of polystyrene. (b) Find the
A constant potential difference of 12 V is maintained between the terminals of a 0.25-µF, parallel-plate, air capacitor. (a) A sheet of Mylar is inserted between the plates of the capacitor,
When a 360-nF air capacitor (1 nF = 10-9 F) is connected to a power supply, the energy stored in the capacitor is 1.85 X 10-5 J. While the capacitor is kept connected to the power supply, a slab of
A parallel-plate capacitor has capacitance C = 12.5 pF when the volume between the plates is filled with air. The plates are circular, with radius 3.00 cm. The capacitor is connected to a battery and
A 12.5-µF capacitor is connected to a power supply that keeps a constant potential difference of 24.0 V across the plates. A piece of material having a dielectric constant of 3.75 is placed between
A parallel-plate capacitor has plates with area 0.0225 m2 separated by 1.00 mm of Teflon. (a) Calculate the charge on the plates when they are charged to a potential difference of 12.0 V. (b) Use
A parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant K. The magnitude of the charge on each plate is Q. Each plate has area a. and the distance
A parallel-plate air capacitor is made by using two plates 16 cm square, spaced 4.7 mm apart. It is connected to a 12-V battery. (a) What is the capacitance? (b) What is the charge on each plate? (c)
Suppose the battery in Problem 24.50 remains connected while the plates are pulled apart. What are the answers then to parts (a)-{d) after the plates have been pulled apart?
Cell Membranes Cell membranes (the walled enclosure around a cell) are typically about 7.5 nm thick. They are partially permeable to allow charged material to pass in and out, as needed. Equal but
Electronic flash units for cameras contain a capacitor for storing the energy used to produce the flash. In one such unit, the flash lasts for 675S with an average light power output of 2.70 X 105W.
In one type of computer keyboard, each key holds a small metal plate that serves as one plate of a parallel-plate, air-filled capacitor. When the key is depressed, the plate separation decreases and
Consider a cylindrical capacitor like that shown in Fig. Let d = rb - rc. be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different,
In Fig let C1 = 9.0µF, C2 = 4.0µF, and Vab = 28V. Suppose the charged capacitors are disconnected from the source and from each other, and then reconnected to each other with plates of opposite
For the capacitor network shown in Fig, the potential difference across ab is 12.0 V. Find(a) The total energy stored in this network and(b) The energy stored in the 4.80-µF capacitor.
Several 0.25-µF capacitors are available. The voltage across each is not to exceed 600 V. You need to make a capacitor with capacitance 0.25 µF to be connected across a potential difference of 960
In Fig, C1 = C5 = 8.4µF and C2 = C3 = C6 = 4.2µF. The applied potential is Vab = 220 V.(a) What is the equivalent capacitance of the network between points a and b?(b) Calculate the
The capacitors in Fig. are initially uncharged and are connected, as in the diagram, with switch S open. The applied potential difference is Vab = +210 V.(a) What is the potential difference Vcd?(b)
Three capacitors having capacitances of 8.4, 8.4, and 4.2µF are connected in series across a 36-V potential difference. (a) What is the charge on the 4.2-µF capacitor? (b) What is the total energy
Capacitance of a Thundercloud The charge center of a thundercloud, drifting 3.0 km above the earth's surface, contains 20 C of negative charge. Assuming the charge center has a radius of 1.0 km, and
In Fig, each capacitance C1 is 6.9 µF, and each capacitance C2 is 4.6 µF.(a) Compute the equivalent capacitance of the network between points a and b.(b) Compute the charge on each of the
Each combination of capacitors between points a and b in Fig is first connected across a 120-V battery, charging the combination to 120 V. These combinations are then connected to make the circuits
A parallel-plate capacitor with only air between the plates is charged by connecting it to a battery. The capacitor is then disconnected from the battery, without any of the charge leaving the
An air capacitor is made by using two flat plates, each with area A, separated by a distance d. Then a metal slab has thickness a (less than d) and the same shape and size as the plates are inserted
Capacitance of the Earth (a) Discuss how the concept of capacitance can also be applied to a single conductor. (b) Use Eq. (24.1) to show that C = 4πє0R for a solid conducting sphere of
A solid conducting sphere of radius R carries a charge Q. Calculate the electric-field energy density at a point a distance r from the center of the sphere for (a) r < R and (b) r > R. (c) Calculate
Earth-Ionosphere Capacitance, The earth can be considered as a single-conductor capacitor (see Problem 24.67). It can also be considered in combination with a charged layer of the atmosphere, the
The inner cylinder of a long, cylindrical capacitor has radius ra and linear charge density + λ. It is surrounded by a coaxial cylindrical conducting shell with inner radius rb and linear charge
A parallel-plate capacitor has the space between the plates filled with two slabs of dielectric, one with constant K1 and one with constant K2 (Fig). Each slab has thickness d/2, where d is the plate
A parallel-plate capacitor has the space between the plates filled with two slabs of dielectric, one with constant K1 and one with constant K2 (Fig). The thickness of each slab is the same as the
Capacitors in networks cannot always be grouped into simple series or parallel combinations. As an example, Fig .a shows three capacitors Cx, Cy, and Cz in a delta network, so called because of its
The parallel-plate air capacitor in Fig consists of two horizontal conducting plates of equal area A. The bottom plate rests on a fixed support, and the top plate is suspended by four springs with
Two square conducting plates with sides of length L are separated. By a distance D. A dielectric slab with constant K with dimensions L X L X D is inserted a distance x into the space between the
An isolated spherical capacitor has charge + Q on its inner conductor (radius ra and charge -Q on its outer conductor (radius rb) Half of the volume between the two conductors is then filled with a
Three square metal plates A, B, and C, each 120 cm on a side and 1.50 mm thick, are arranged as in Fig. 24.43. The plates are separated by sheets of paper 0.45 mm thick and with dielectric constant
A fuel gauge uses a capacitor to determine the height of the fuel in a tank. The effective dielectric constant Keff changes from a value of 1 when the tank is empty to a value of K, the dielectric
A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h?
A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80 min. Silver contains 5.8 X 1028 free electrons per cubic meter. (a) What is the current in the wire? (b) What is the magnitude of
A 5.00-A current runs through a 12-gauge copper wire (diameter 2.05 mm) and through a light bulb. Copper has 85 X 1028 free electrons per cubic meter. (a) How many electrons pass through the light
An 18-gauge wire (diameter 1.02 mm) carries a current with a current density of 1.50 X 106 A/m2.Calculate (a) The current in the wire and (b) The drift velocity of electrons in the wire.

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