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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

A non-conducting wall carries a uniform charge density of 8.60 %C/cm2. What is the electric field 7.00 cm in front of the wall? Does your result change as the distance from the wall is varied?
Consider a long cylindrical charge distribution of radius R with a uniform charge density 1. Find the electric field at distance r from the axis where r < R.
A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find the magnitude of the
Consider a thin spherical shell of radius 14.0 cm with a total charge of 32.0 %C distributed uniformly on its surface. Find the electric field (a) 10.0 cm and (b) 20.0 cm from the center of the
In nuclear fission, a nucleus of uranium-238, which contains 92 protons, can divide into two smaller spheres, each having 46 protons and a radius of 5.90 & 10'15 m. What is the magnitude of the
Fill two rubber balloons with air. Suspend both of them from the same point and let them hang down on strings of equal length. Rub each with wool or on your hair, so that they hang apart with a
An insulating solid sphere of radius a has a uniform volume charge density and carries a total positive charge Q. A spherical Gaussian surface of radius r, which shares a common center with the
A uniformly charged, straight filament 7.00 m in length has a total positive charge of 2.00 %C. An uncharged cardboard cylinder 2.00 cm in length and 10.0 cm in radius surrounds the filament at its
An insulating sphere is 8.00 cm in diameter and carries a 5.70-%C charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with
A large flat horizontal sheet of charge has a charge per unit area of 9.00 %C/m2. Find the electric field just above the middle of the sheet.
The charge per unit length on a long, straight filament is '90.0 %C/m. Find the electric field (a) 10.0 cm, (b) 20.0 cm, and (c) 100 cm from the filament, where distances are measured
A long, straight metal rod has a radius of 5.00 cm and a charge per unit length of 30.0 nC/m Find the electric field (a) 3.00 cm, (b) 10.0 cm, and (c) 100 cm from the axis of the rod, where
On a clear, sunny day, a vertical electric field of about 130 N/C points down over flat ground. What is the surface charge density on the ground for these conditions?
A very large, thin, flat plate of aluminum of area A has a total charge Q uniformly distributed over its surfaces. Assuming the same charge is spread uniformly over the upper surface of an otherwise
A solid copper sphere of radius 15.0 cm carries a charge of 40.0 nC. Find the electric field (a) 12.0 cm, (b) 17.0 cm, and (c) 75.0 cm from the center of the sphere (d) What If? How would
A square plate of copper with 50.0-cm sides has no net charge and is placed in a region of uniform electric field of 80.0 kN/C directed perpendicularly to the plate. Find (a) The charge density of
A solid conducting sphere of radius 2.00 cm has a charge of 8.00 %C. 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 total
Two identical conducting spheres each having a radius of 0.500 cm are connected by a light 2.00-m-long conducting wire. A charge of 60.0 %C is placed on one of the conductors. Assume that the surface
The electric field on the surface of an irregularly shaped conductor varies from 56.0 kN/C to 28.0 kN/C. Calculate the local surface charge density at the point on the surface where the radius of
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of 3, and the cylinder has a net charge per unit
A conducting spherical shell of radius 15.0 cm carries a net charge of -6.40 C uniformly distributed on its surface. Find the electric field at points (a) Just outside the shell and (b) Inside
A thin square conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 x 10-8 C is placed on the plate. Find (a) The charge density on the plate, (b) The electric field just
A conducting spherical shell of inner radius a and outer radius b carries a net charge Q. A point charge q is placed at the center of this shell. Determine the surface charge density on (a) The
A hollow conducting sphere is surrounded by a larger concentric spherical conducting shell. The inner sphere has charge -Q, and the outer shell has net charge +3Q. The charges are in electrostatic
A positive point charge is at a distance R/2 from the center of an uncharged thin conducting spherical shell of radius R. Sketch the electric field lines set up by this arrangement both inside and
A sphere of radius R surrounds a point charge Q, located at its center. (a) Show that the electric flux through a circular cap of half-angle ) (Fig. P24.53) isWhat is the flux for?(b) θ =
A non-uniform electric field is given by the expression E = ayi + bzjˆ + cxkˆ, where a, b, and c are constants. Determine the electric flux through a rectangular surface in the xy plane, extending
A solid insulating sphere of radius a carries a net positive charge 3Q, uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b
Consider two identical conducting spheres whose surfaces are separated by a small distance. One sphere is given a large net positive charge while the other is given a small net positive charge. It is
A solid, insulating sphere of radius a has a uniform charge density 1 and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and
For the configuration shown in Figure P24.57, suppose that a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose that the electric field at a point 10.0 cm from the center is measured to be
A particle of mass m and charge q moves at high speed along the x axis. It is initially near x = -7, and it ends up near x = 7. A second charge Q is fixed at the point x = 0, y = -d. As the moving
An early (incorrect) model of the hydrogen atom, suggested by J. J. Thomson, proposed that a positive cloud of charge $e was uniformly distributed throughout the volume of a sphere of radius R, with
An infinitely long cylindrical insulating shell of inner radius a and outer radius b has a uniform volume charge density 1. A line of uniform linear charge density A is placed along the axis of the
Two infinite, non-conducting sheets of charge are parallel to each other, as shown in Figure P24.62. The sheet on the left has a uniform surface charge density a, and the one on the right has a
A sphere of radius 2a is made of a non-conducting material that has a uniform volume charge density 1. (Assume that the material does not affect the electric field.) A spherical cavity of radius a is
A uniformly charged spherical shell with surface charge density 4 contains a circular hole in its surface. The radius of the hole is small compared with the radius of the sphere. What is the electric
A closed surface with dimensions a = b = 0.400 m and c = 0.600 m is located as in Figure P24.66. The left edge of the closed surface is located at position x = a. The electric field throughout the
A solid insulating sphere of radius R has a non-uniform charge density that varies with r according to the expression 1 = Ar 2, where A is a constant and r < R is measured from the center of the
A point charge Q is located on the axis of a disk of radius R at a distance b from the plane of the disk (Fig. P24.68). Show that if one fourth of the electric flux from the charge passes through the
A spherically symmetric charge distribution has a charge density given by p = a/r, where a is constant. Find the electric field as a function of r. (Suggestion: The charge within a sphere of radius R
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as where p0, a, and b are positive constants and r is the distance from the axis of the
A slab of insulating material has a non-uniform positive charge density p = Cx2, where x is measured from the center of the slab as shown in Figure P24.71, and C is a constant. The slab is infinite
(a) Using the mathematical similarity between Coulomb’s law and Newton’s law of universal gravitation, show that Gauss’s law for gravitation can be written as where min is the net mass inside
(a) How much charge is on each plate of a 4.00-μF capacitor when it is connected to a 12.0-V battery? (b) If this same capacitor is connected to a 1.50-V battery, what charge is stored?
Two conductors having net charges of + 10.0μC and -10.0 μC have a potential difference of 10.0 V between them. (a) Determine the capacitance of the system. (b) What is the potential
An isolated charged conducting sphere of radius 12.0 cm creates an electric field of 4.90 x 104 N/C at a distance 21.0 cm from its center. (a) What is its surface charge density? (b) What is its
(a) If a drop of liquid has capacitance 1.00 pF, what is its radius? (b) If another drop has radius 2.00 mm, what is its capacitance? (c) What is the charge on the smaller drop if its potential
Two conducting spheres with diameters of 0.400 m and 1.00 m are separated by a distance that is large compared with the diameters. The spheres are connected by a thin wire and are charged to 7.00 %C.
Regarding the Earth and a cloud layer 800 m above the Earth as the “plates’’ of a capacitor, calculate the capacitance. Assume the cloud layer has an area of 1.00 km2 and that the air between
An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.80 mm. A 20.0-V potential difference is applied to these plates. Calculate (a)
A 1-megabit computer memory chip contains many 60.0-f 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
When a potential difference of 150 V is applied to the plates of a parallel-plate capacitor, the plates carry a surface charge density of 30.0 nC/cm2. What is the spacing between the plates?
A variable air capacitor used in a radio tuning circuit is made of N semicircular plates each of radius R and positioned a distance d from its neighbors, to which it is electrically connected. As
A 50.0-m length of coaxial cable has an inner conductor that has a diameter of 2.58 mm and carries a charge of 8.10 μC. The surrounding conductor has an inner diameter of 7.27 mm and a charge of
A 20.0-%F spherical capacitor is composed of two concentric metal spheres, one having a radius twice as large as the other. The region between the spheres is a vacuum. Determine the volume of this
An air-filled spherical capacitor is constructed with inner and outer shell radii of 7.00 and 14.0 cm, respectively. (a) Calculate the capacitance of the device. (b) What potential difference
A small object of mass m carries a charge q and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plate separation is d. If the thread makes an angle θ with
Find the capacitance of the Earth. (Suggestion: The outer conductor of the “spherical capacitor’’ may be considered as a conducting sphere at infinity where V approaches zero.)
Two capacitors, C1 = 5.00 μF and C2 = 12.0μ F, are connected in parallel, and the resulting combination is connected to a 9.00-V battery. (a) What is the equivalent capacitance of the
What If? The two capacitors of Problem 16 are now connected in series and to a 9.00-V battery. Find (a) The equivalent capacitance of the combination, (b) The potential difference across each
Evaluate the equivalent capacitance of the configuration shown in Figure P26.18. All the capacitors are identical, and each has capacitance C.
Two capacitors when connected in parallel give an equivalent capacitance of 9.00 pF and give an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor?
Two capacitors when connected in parallel give an equivalent capacitance of Cp and an equivalent capacitance of Cs when connected in series. What is the capacitance of each capacitor?
Four capacitors are connected as shown in Figure P26.21.(a) Find the equivalent capacitance between points a and b.(b) Calculate the charge on each capacitor if ∆Vab = 15.0 V.
Three capacitors are connected to a battery as shown in Figure P26.22. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C.(a) What is the equivalent capacitance of this set of capacitors?(b) State
Consider the circuit shown in Figure P26.23, where C1 = 6.00 μF, C2 = 3.00 μF, and ∆V = 20.0 V. Capacitor C1 is first charged by the closing of switch S1. Switch S1 is then opened,
According to its design specification, the timer circuit delaying the closing of an elevator door is to have a capacitance of 32.0 %F between two points A and B. (a) When one circuit is being
A group of identical capacitors is connected first in series and then in parallel. The combined capacitance in parallel is 100 times larger than for the series connection. How many capacitors are in
Consider three capacitors C1, C2, C3, and a battery. If C1 is connected to the battery, the charge on C1 is 30.8 %C. Now C1 is disconnected, discharged, and connected in series with C2. When the
Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P26.27. Take C1 = 5.00 μF, C2 = 10.0 μF, and C3 = 2.00 μF.
For the network described in the previous problem, if the potential difference between points a and b is 60.0 V, what charge is stored on C3?
Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure P26.29.
Some physical systems possessing capacitance continuously distributed over space can be modeled as an infinite array of discrete circuit elements. Examples are a microwave waveguide and the axon of a
(a) A 3.00-%F capacitor is connected to a 12.0-V battery. How much energy is stored in the capacitor? (b) If the capacitor had been connected to a 6.00-V battery, how much energy would have been
The immediate cause of many deaths is ventricular fibrillation, uncoordinated quivering of the heart as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the
Two capacitors, C1 = 25.0 μF and C2 = 5.00μF, are connected in parallel and charged with a 100-V power supply. (a) Draw a circuit diagram and calculate the total energy stored in the two
A parallel-plate capacitor is charged and then disconnected from a battery. By what fraction does the stored energy change (increase or decrease) when the plate separation is doubled?
As a person moves about in a dry environment, electric charge accumulates on his body. Once it is at high voltage, either positive or negative, the body can discharge via sometimes noticeable sparks
A uniform electric field E = 3 000 V/m exists within a certain region. What volume of space contains an energy equal to 1.00 x 10-7 J? Express your answer in cubic meters and in liters.
A parallel-plate capacitor has a charge Q and plates of area A. What force acts on one plate to attract it toward the other plate? Because the electric field between the plates is E = Q /A) 0, you
The circuit in Figure P26.38 consists of two identical parallel metal plates connected by identical metal springs to a 100-V battery. With the switch open, the plates are uncharged, are separated by
A certain storm cloud has a potential of 1.00 x 108 V relative to a tree. If, during a lightning storm, 50.0 C of charge is transferred through this potential difference and 1.00% of the energy is
Two identical parallel-plate capacitors, each with capacitance C, are charged to potential difference ∆V and connected in parallel. Then the plate separation in one of the capacitors is
Show that the energy associated with a conducting sphere of radius R and charge Q surrounded by a vacuum is U = keQ2/2R.
Consider two conducting spheres with radii R1 and R2. They are separated by a distance much greater than either radius. A total charge Q is shared between the spheres, subject to the condition that
Determine (a) the capacitance and (b) The maximum potential difference that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 1.75 cm2 and plate separation of 0.040
(a) How much charge can be placed on a capacitor with air between the plates before it breaks down, if the area of each of the plates is 5.00 cm2? (b) What If? Find the maximum charge if
A commercial capacitor is to be constructed as shown in Figure 26.17a. This particular capacitor is made from two strips of aluminum separated by a strip of paraffin-coated paper. Each strip of foil
The supermarket sells rolls of aluminum foil, of plastic wrap, and of waxed paper. Describe a capacitor made from supermarket materials. Compute order-of-magnitude estimates for its capacitance and
A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 250 V and disconnected from the source. The
A wafer of titanium dioxide (1 = 173) of area 1.00 cm2 has a thickness of 0.100 mm. Aluminum is evaporated on the parallel faces to form a parallel-plate capacitor. (a) Calculate the capacitance.
Each capacitor in the combination shown in Figure P26.49 has a breakdown voltage of 15.0 V. What is the breakdown voltage of the combination?
A small rigid object carries positive and negative 3.50-nC charges. It is oriented so that the positive charge has coordinates (-1.20 mm, 1.10 mm) and the negative charge is at the point (1.40 mm,
A small object with electric dipole moment p is placed in a non-uniform electric field E = E(x)i. That is, the field is in the x direction and its magnitude depends on the coordinate x. Let θ
A detector of radiation called a Geiger tube consists of a closed, hollow, conducting cylinder with a fine wire along its axis. Suppose that the internal diameter of the cylinder is 2.50 cm and that
The general form of Gauss’s law describes how a charge creates an electric field in a material, as well as in vacuum. It is where ) = 1)0 is the permittivity of the material. (a) A sheet with
For the system of capacitors shown in Figure P26.54, find (a) The equivalent capacitance of the system, (b) The potential across each capacitor, (c) The charge on each capacitor, and (d) The
Four parallel metal plates P1, P2, P3, and P4, each of area 7.50 cm2, are separated successively by a distance d = 1.19 mm, as shown in Figure P26.55. P1 is connected to the negative terminal of a
One conductor of an overhead electric transmission line is a long aluminum wire 2.40 cm in radius. Suppose that at a particular moment it carries charge per length 1.40 μC/m and is at potential

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