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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Two large parallel metal plates are oriented horizontally and separated by a distance 3d. A grounded conducting wire joins them, and initially each plate carries no charge. Now a third identical
A 2.00-nF parallel-plate capacitor is charged to an initial potential difference ∆Vi = 100 V and then isolated. The dielectric material between the plates is mica, with a dielectric constant of
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
A 10.0-μF capacitor has plates with vacuum between them. Each plate carries a charge of magnitude 1 000 μC. A particle with charge -3.00 μC and mass 2.00 x 10-16 kg is fired from the
A parallel-plate capacitor is constructed by filling the space between two square plates with blocks of three dielectric materials, as in Figure P26.61. You may assume that ℓ, d. (a) Find an
A 10.0-μF capacitor is charged to 15.0 V. It is next connected in series with an uncharged 5.00-%F capacitor. The series combination is finally connected across a 50.0-V battery, as diagrammed in
(a) Two spheres have radii a and b and their centers are a distance d apart. Show that the capacitance of this system is provided that d is large compared with a and b. (Suggestion: Because the
A capacitor is constructed from two square plates of sides ℓ and separation d. A material of dielectric constant 1 is inserted a distance x into the capacitor, as shown in Figure P26.64. Assume
A capacitor is constructed from two square plates of sides ℓ and separation d, as suggested in Figure P26.64. You may assume that d is much less than ℓ. The plates carry charges +Q 0 and
When considering the energy supply for an automobile, the energy per unit mass of the energy source is an important parameter. Using the following data, compare the energy per unit mass (J/kg) for
An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 V. When the charged capacitor is then connected in parallel to an uncharged 10.0-μF capacitor, the
To repair a power supply for a stereo amplifier, an electronics technician needs a 100-μF capacitor capable of withstanding a potential difference of 90 V between the plates. The only available
A parallel-plate capacitor of plate separation d is charged to a potential difference V0. A dielectric slab of thickness d and dielectric constant k is introduced between the plates while the battery
A vertical parallel-plate capacitor is half filled with a dielectric for which the dielectric constant is 2.00 (Fig. P26.70a). When this capacitor is positioned horizontally, what fraction of it
Capacitors C1 = 6.00 F and C2 = 2.00 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
Calculate the equivalent capacitance between the points a and b in Figure P26.72. Note that this is not a simple series or parallel combination. (Suggestion: Assume a potential difference ℓ V
The inner conductor of a coaxial cable has a radius of 0.800 mm, and the outer conductor’s inside radius is 3.00 mm. The space between the conductors is filled with polyethylene, which has a
You are optimizing coaxial cable design for a major manufacturer. Show that for a given outer conductor radius b, maximum potential difference capability is attained when the radius of the inner
Determine the equivalent capacitance of the combination shown in Figure P26.75. (Suggestion: Consider the symmetry involved.)
Consider two long, parallel, and oppositely charged wires of radius d with their centers separated by a distance D. Assuming the charge is distributed uniformly on the surface of each wire, show that
Example 26.2 explored a cylindrical capacitor of length ℓ and radii a and b of the two conductors. In the What If? Section, it was claimed that increasing ℓ by 10% is more effective in
In a particular cathode ray tube, the measured beam current is 30.0 μA. How many electrons strike the tube screen every 40.0 s?
A teapot with a surface area of 700 cm2 is to be silver plated. It is attached to the negative electrode of an electrolytic cell containing silver nitrate (Ag, + NO3 -). If the cell is powered by a
Suppose that the current through a conductor decreases exponentially with time according to the equation I (t) = Ioe-t/r where I0 is the initial current (at t = 0), and + is a constant having
In the Bohr model of the hydrogen atom, an electron in the lowest energy state follows a circular path 5.29 x 10-11 m from the proton. (a) Show that the speed of the electron is 2.19 x 106 m/s.
A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is w. What average current does this rotating charge represent?
The quantity of charge q (in coulombs) that has passed through a surface of area 2.00 cm2 varies with time according to the equation q = 4t3 + 5t + 6, where t is in seconds. (a) What is the
An electric current is given by the expression I (t) = 100 sin (120πt), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = (1/240) s?
Figure P27.8 represents a section of a circular conductor of non-uniform diameter carrying a current of 5.00 A. The radius of cross section A1 is 0.400 cm.(a) What is the magnitude of the current
The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.00 mm. (a) The beam current is 8.00 /A. Find the current density in the beam,
A Van de Graaff generator produces a beam of 2.00-MeV deuterons, which are heavy hydrogen nuclei containing a proton and a neutron. (a) If the beam current is 10.0 μA, how far apart are the
An aluminum wire having a cross-sectional area of 4.00 x 10-6 m2 carries a current of 5.00 A. Find the drift speed of the electrons in the wire. The density of aluminum is 2.70 g/cm3. Assume that one
Calculate the current density in a gold wire at 20°C, if an electric field of 0.740 V/m exists in the wire.
A lightbulb has a resistance of 240 when operating with a potential difference of 120 V across it. What is the current in the lightbulb?
A resistor is constructed of a carbon rod that has a uniform cross-sectional area of 5.00 mm2. When a potential difference of 15.0 V is applied across the ends of the rod, the rod carries a current
A 0.900-V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of 0.600 mm2. What is the current in the wire?
A conductor of uniform radius 1.20 cm carries a current of 3.00 A produced by an electric field of 120 V/m. What is the resistively of the material?
Suppose that you wish to fabricate a uniform wire out of 1.00 g of copper. If the wire is to have a resistance of R = 0.500, and if all of the copper is to be used, what will be (a) The length and
Gold is the most ductile of all metals. For example, one gram of gold can be drawn into a wire 2.40 km long. What is the resistance of such a wire at 20°C? You can find the necessary reference
(a) Make an order-of-magnitude estimate of the resistance between the ends of a rubber band. (b) Make an order-of-magnitude estimate of the resistance between the ‘heads’ and ‘tails’ sides
A solid cube of silver (density = 10.5 g/cm3) has a mass of 90.0 g. (a) What is the resistance between opposite faces of the cube? (b) Assume each silver atom contributes one conduction electron.
A metal wire of resistance R is cut into three equal pieces that are then connected side by side to form a new wire the length of which is equal to one-third the original length. What is the
Aluminum and copper wires of equal length are found to have the same resistance. What is the ratio of their radii?
A current density of 6.00 x 10-13 A/m2 exists in the atmosphere at a location where the electric field is 100 V/m. Calculate the electrical conductivity of the Earth’s atmosphere in this region.
The rod in Figure P27.24 is made of two materials. The figure is not drawn to scale. Each conductor has a square cross section 3.00 mm on a side. The first material has a resistivity of 4.00 x 10-3
If the magnitude of the drift velocity of free electrons in a copper wire is 7.84 x 10-4 m/s, what is the electric field in the conductor?
If the current carried by a conductor is doubled, what happens to the (a) Charge carrier density? (b) Current density? (c) Electron drift velocity? (d) Average time interval between
Use data from Example 27.1 to calculate the collision mean free path of electrons in copper. Assume the average thermal speed of conduction electrons is 8.60 x 105 m/s.
While taking photographs in Death Valley on a day when the temperature is 58.0°C, Bill Hiker finds that a certain voltage applied to a copper wire produces a current of 1.000 A. Bill then travels to
A certain lightbulb has a tungsten filament with a resistance of 19.0 ' when cold and 140 ' when hot. Assume that the resistivity of tungsten varies linearly with temperature even over the large
A carbon wire and a Nichrome wire are connected in series, so that the same current exists in both wires. If the combination has a resistance of 10.0 k' at 0°C, what is the resistance of each wire
An aluminum wire with a diameter of 0.100 mm has a uniform electric field of 0.200 V/m imposed along its entire length. The temperature of the wire is 50.0°C. Assume one free electron per atom. (a)
An aluminum rod has a resistance of 1.234 ' at 20.0°C. Calculate the resistance of the rod at 120°C by accounting for the changes in both the resistivity and the dimensions of the rod.
What is the fractional change in the resistance of an iron filament when its temperature changes from 25.0°C to 50.0°C?
The resistance of a platinum wire is to be calibrated for low-temperature measurements. A platinum wire with resistance 1.00 ' at 20.0°C is immersed in liquid nitrogen at 77 K (-196°C). If the
The temperature of a sample of tungsten is raised while a sample of copper is maintained at 20.0°C. At what temperature will the resistivity of the tungsten be four times that of the copper?
A toaster is rated at 600 W when connected to a 120-V source. What current does the toaster carry, and what is its resistance?
A Van de Graaff generator (see Figure 25.29) is operating so that the potential difference between the high-voltage electrode B and the charging needles at A is 15.0 kV. Calculate the power required
In a hydroelectric installation, a turbine delivers 1 500 hp to a generator, which in turn transfers 80.0% of the mechanical energy out by electrical transmission? Under these conditions, what
What is the required resistance of an immersion heater that increases the temperature of 1.50 kg of water from 10.0°C to 50.0°C in 10.0 min while operating at 110 V?
One rechargeable battery of mass 15.0 g delivers to a CD player an average current of 18.0 mA at 1.60 V for 2.40 h before the battery needs to be recharged. The recharger maintains a potential
Suppose that a voltage surge produces 140 V for a moment. By what percentage does the power output of a 120-V, 100-W lightbulb increase Assume that its resistance does not change.
A 500-W heating coil designed to operate from 110 V is made of Nichrome wire 0.500 mm in diameter. (a) Assuming that the resistivity of the Nichrome remains constant at its 20.0°C value, find the
A coil of Nichrome wire is 25.0 m long. The wire has a diameter of 0.400 mm and is at 20.0°C. If it carries a current of 0.500 A, what are (a) The magnitude of the electric field in the wire, and
Batteries are rated in terms of ampere-hours (A ∙ h). For example, a battery that can produce a current of 2.00 A for 3.00 h is rated at 6.00 A ∙ h. (a) What is the total energy, in
A 10.0-V battery is connected to a 120-' resistor. Ignoring the internal resistance of the battery, calculate the power delivered to the resistor.
Residential building codes typically require the use of 12-gauge copper wire (diameter 0.205 3 cm) for wiring receptacles. Such circuits carry currents as large as 20 A. A wire of smaller diameter
An 11.0-W energy-efficient fluorescent lamp is designed to produce the same illumination as a conventional 40.0-W incandescent lightbulb. How much money does the user of the energy-efficient lamp
We estimate that 270 million plug-in electric clocks are in the United States, approximately one clock for each person. The clocks convert energy at the average rate 2.50 W. To supply this energy,
Compute the cost per day of operating a lamp that draws a current of 1.70 A from a 110-V line. Assume the cost of energy from the power company is $0.060 0/kWh.
The heating element of a coffee maker operates at 120 V and carries a current of 2.00 A. Assuming that the water absorbs all of the energy delivered to the resistor, calculate how long it takes to
A certain toaster has a heating element made of Nichrome wire. When the toaster is first connected to a 120-V source (and the wire is at a temperature of 20.0°C), the initial current is 1.80 A.
The cost of electricity varies widely through the United States; $0.120/kWh is one typical value. At this unit price, calculate the cost of (a) Leaving a 40.0-W porch light on for two weeks while
Make an order-of-magnitude estimate of the cost of one person’s routine use of a hair dryer for 1 yr. If you do not use a blow dryer yourself, observe or interview someone who does. State the
One lightbulb is marked ‘25W 120 V,’ and another ‘100 W 120 V’; this means that each bulb has its respective power delivered to it when plugged into a constant 120-V potential difference.
A charge Q is placed on a capacitor of capacitance C. The capacitor is connected into the circuit shown in Figure P27.55, with an open switch, a resistor, and an initially uncharged capacitor of
A high-voltage transmission line with a diameter of 2.00 cm and a length of 200 km carries a steady current of 1 000 A. If the conductor is copper wire with a free charge density of 8.49 = 1028
A more general definition of the temperature coefficient of resistivity is where % is the resistivity at temperature T0(a) Assuming that - is constant, show that where %0 is the resistivity at
A high-voltage transmission line carries 1 000 A starting at 700 kV for a distance of 100 mi. If the resistance in the wire is 0.500 Ω/mi, what is the power loss due to resistive losses?
An experiment is conducted to measure the electrical resistivity of Nichrome in the form of wires with different lengths and cross-sectional areas. For one set of measurements, a student uses
An electric utility company supplies a customer’s house from the main power lines (120 V) with two copper wires, each of which is 50.0 m long and has a resistance of 0.108 ' per 300 m. (a) Find
A straight cylindrical wire lying along the x axis has a length of 0.500 m and a diameter of 0.200 mm. It is made of a material that obeys Ohm’s law with a resistivity of o = 4.00 x 10-8 '(m.
A straight cylindrical wire lying along the x axis has a length L and a diameter d. It is made of a material that obeys Ohm’s law with a resistivity %. Assume that potential V is maintained at x =
The potential difference across the filament of a lamp is maintained at a constant level while equilibrium temperature is being reached. It is observed that the steady-state current in the lamp is
The current in a resistor decreases by 3.00 A when the voltage applied across the resistor decreases from 12.0 V to 6.00 V. Find the resistance of the resistor.
An electric car is designed to run off a bank of 12.0-V batteries with total energy storage of 2.00 x 107 J. (a) If the electric motor draws 8.00 kW, what is the current delivered to the motor?
When a straight wire is heated, its resistance is given by R = R0 [1 + a (T - T0)] according to Equation 27.21, where - is the temperature coefficient of resistivity. (a) Show that a more precise
The temperature coefficients of resistivity in Table 27.1 were determined at a temperature of 20°C. What would they be at 0°C? Note that the temperature coefficient of resistivity at 20°C
An oceanographer is studying how the ion concentration in sea water depends on depth. She does this by lowering into the water a pair of concentric metallic cylinders (Fig. P27.68) at the end of a
In a certain stereo system, each speaker has a resistance of 4.00 '. The system is rated at 60.0 W in each channel, and each speaker circuit includes a fuse rated 4.00 A. Is this system adequately
A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 20.7) and the flow of electric charge because of a potential difference. The energy dQ and
Material with uniform resistivity % is formed into a wedge as shown in Figure P27.71. Show that the resistance between face A and face B of this wedge is
A material of resistivity p is formed into the shape of a truncated cone of altitude h as shown in Figure P27.72. The bottom end has radius b, and the top end has radius a. Assume that the current is
The dielectric material between the plates of a parallel plate capacitor always has some nonzero conductivity &. Let A represent the area of each plate and d the distance between them. Let 4
The current–voltage characteristic curve for a semiconductor diode as a function of temperature T is given by the equation I = I0 (ee∆/kBT – 1) Here the first symbol e represents
A parallel-plate capacitor consists of square plates of edge length ℓ that are separated by a distance d, where d
A battery has an emf of 15.0 V. The terminal voltage of the battery is 11.6 V when it is delivering 20.0 W of power to an external load resistor R. (a) What is the value of R? (b) What is the
(a) What is the current in a 5.60-Ω resistor connected to a battery that has a 0.200-Ω internal resistance if the terminal voltage of the battery is 10.0 V? (b) What is the emf of the
Two 1.50-V batteries—with their positive terminals in the same direction—are inserted in series into the barrel of a flashlight. One battery has an internal resistance of 0.255 Ω, the other
An automobile battery has an emf of 12.6 V and an internal resistance of 0.080 0 Ω. The headlights together present equivalent resistance 5.00 Ω (assumed constant). What is the potential

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