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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Two particles, with charges of 20.0 nC and - 20.0 nC, are placed at the points with coordinates (0, 4.00 cm) and (0, -4.00 cm), as shown in Figure P25.28. A particle with charge 10.0 nC is located at
A light unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and then
Two point charges of equal magnitude are located along the y axis equal distances above and below the x axis, as shown in Figure P25.30.(a) Plot a graph of the potential at points along the x axis
A small spherical object carries a charge of 8.00 nC. At what distance from the center of the object is the potential equal to 100 V? 50.0 V? 25.0 V? Is the spacing of the equipotentials proportional
In 1911 Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles from thin sheets of gold. An alpha particle, having charge + 2e and
An electron starts from rest 3.00 cm from the center of a uniformly charged insulating sphere of radius 2.00 cm and total charge 1.00 nC. What is the speed of the electron when it reaches the surface
Calculate the energy required to assemble the array of charges shown in Figure P25.34, where a = 0.200 m, b = 0.400 m, and q = 6.00 +C.
Four identical particles each have charge q and mass m. They are released from rest at the vertices of a square of side L. How fast is each charge moving when their distance from the center of the
How much work is required to assemble eight identical point charges, each of magnitude q, at the corners of a cube of side s?
The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 10.0 V and b = -7.00 V/m. Determine (a) The potential at x = 0, 3.00 m, and 6.00 m, and (b) The magnitude and
The electric potential inside a charged spherical conductor of radius R is given by V = keQ/R, and the potential outside is given by V = keQ/r. Using Er = -dV/dr, derive the electric field (a) inside
Over a certain region of space, the electric potential is V = 5x - 3x2y + 2yz2. Find the expressions for the x, y, and z components of the electric field over this region. What is the magnitude of
Figure P25.40 shows several equipotential lines each labeled by its potential in volts. The distance between the lines of the square grid represents 1.00 cm.(a) Is the magnitude of the field larger
It is shown in Example 25.7 that the potential at a point P a distance a above one end of a uniformly charged rod of length ℓ lying along the x axis is Use this result to derive an expression
Consider a ring of radius R with the total charge Q spread uniformly over its perimeter. What is the potential difference between the point at the center of the ring and a point on its axis a
A rod of length L (Fig P25.43) lies along the x axis with its left end at the origin. It has a non-uniform charge density 1 = 5x, where 5 is a positive constant. (a) What are the units of 5? (b)
For the arrangement described in the previous problem, calculate the electric potential at point B, which lies on the perpendicular bisector of the rod a distance b above the x axis.
Compare this problem with Problem 33 in Chapter 23. A uniformly charged insulating rod of length 14.0 cm is bent into the shape of a semicircle as shown in Figure P23.33. The rod has a total charge
Calculate the electric potential at point P on the axis of the annulus shown in Figure P25.46, which has a uniform charge density σ.
A wire having a uniform linear charge density A is bent into the shape shown in Figure P25.47. Find the electric potential at point O.
How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?
A spherical conductor has a radius of 14.0 cm and charge of 26.0 μC. Calculate the electric field and the electric potential (a) r = 10.0 cm, (b) r = 20.0 cm, and (c) r = 14.0 cm from the
Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off
Lightning can be studied with a Van de Graaff generator, essentially consisting of a spherical dome on which charge is continuously deposited by a moving belt. Charge can be added until the electric
The spherical dome of a Van de Graaff generator can be raised to a maximum potential of 600 kV; then additional charge leaks off in sparks, by producing dielectric breakdown of the surrounding dry
The liquid-drop model of the atomic nucleus suggests that high-energy oscillations of certain nuclei can split the nucleus into two unequal fragments plus a few neutrons. The fission products acquire
On a dry winter day you scuff your leather-soled shoes across a carpet and get a shock when you extend the tip of one finger toward a metal doorknob. In a dark room you see a spark perhaps 5 mm long.
The Bohr model of the hydrogen atom states that the single electron can exist only in certain allowed orbits around the proton. The radius of each Bohr orbit is r = n2(0.052 9 nm) where n = 1, 2, 3,
An electron is released from rest on the axis of a uniform positively charged ring, 0.100 m from the ring’s center. If the linear charge density of the ring is +0.100 μC/m and the radius of
As shown in Figure P25.57, two large parallel vertical conducting plates separated by distance d are charged so that their potentials are + V0 and -V0. A small conducting ball of mass m and radius R
(a) A uniformly charged cylindrical shell has total charge Q, radius R, and height h. Determine the electric potential at a point a distance d from the right end of the cylinder, as shown in Figure
Calculate the work that must be done to charge a spherical shell of radius R to a total charge Q.
Two parallel plates having charges of equal magnitude but opposite sign are separated by 12.0 cm. Each plate has a surface charge density of 36.0 nC/m2. A proton is released from rest at the positive
A Geiger tube is a radiation detector that essentially consists of a closed, hollow metal cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius rb (Fig.
The results of Problem 61 apply also to an electrostatic precipitator (Figures 25.30 and P25.61). An applied voltage ∆V = Va - Vb = 50.0 kV is to produce an electric field of magnitude 5.50
From Gauss’s law, the electric field set up by a uniform line of charge is E = (A/ πЄθr) r Where is a unit vector pointing radially away from the line and 1 is the linear charge
Four balls, each with mass m, are connected by four non-conducting strings to form a square with side a, as shown in Figure P25.64. The assembly is placed on a horizontal non-conducting frictionless
A point charge q is located at x = -R, and a point charge -2q is located at the origin. Prove that the equipotential surface that has zero potential is a sphere centered at (-4R/3, 0, 0) and having a
Consider two thin, conducting, spherical shells as shown in Figure P25.66. The inner shell has a radius r1 = 15.0 cm and a charge of 10.0 nC. The outer shell has a radius r2 = 30.0 cm and a charge of
The x axis is the symmetry axis of a stationary uniformly charged ring of radius R and charge Q (Fig. P25.67) a point charge Q of mass M is located initially at the center of the ring. When it is
The thin, uniformly charged rod shown in Figure P25.68 has a linear charge density 1. Find an expression for the electric potential at P.
An electric dipole is located along the y axis as shown in Figure P25.69. The magnitude of its electric dipole moment is defined as p =2qa.(a) At a point P, which is far from the dipole (r >> a),
When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E0kˆ, the resulting electric potential is
A disk of radius R (Fig P25.71) has a non-uniform surface charge density 0 = Cr, where C is a constant and r is measured from the center of the disk. Find (by direct integration) the potential at P.
A solid sphere of radius R has a uniform charge density 7 and total charge Q. Derive an expression for its total electric potential energy. (Suggestion: imagine that the sphere is constructed by
Charge is uniformly distributed with a density of 100.0 +C/m3 throughout the volume of a cube 10.00 cm on each edge. (a) Find the electric potential at a distance of 5.000 cm from the center of one
A 50-turn rectangular coil of dimensions 5.00 cm + 10.0 cm is allowed to fall from a position where B = 0 to a new position where B = 0.500 T and the magnetic field is directed perpendicular to the
A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 2.50 T in 1.00 s. What is
A 25-turn circular coil of wire has diameter 1.00 m. It is placed with its axis along the direction of the Earth’s magnetic field of 50.0 /T, and then in 0.200 s it is flipped 180°. An average emf
A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in time according to B =
A strong electromagnet produces a uniform magnetic field of 1.60 T over a cross-sectional area of 0.200 m2. We place a coil having 200 turns and a total resistance of 20.0 Ω around the
A magnetic field of 0.200 T exists within a solenoid of 500 turns and a diameter of 10.0 cm. How rapidly (that is, within what period of time) must the field be reduced to zero, if the average
An aluminum ring of radius 5.00 cm and resistance 3.00 x 10-4 Ω is placed on top of a long air-core solenoid with 1 000 turns per meter and radius 3.00 cm, as shown in Figure P31.7. Over the
An aluminum ring of radius r1 and resistance R is placed around the top of a long air-core solenoid with n turns per meter and smaller radius r 2 as shown in Figure P31.7. Assume that the axial
(a) A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in Figure P31.9.(a) Determine the magnetic flux
A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.00 cm and 1.00 x 103 turns/meter (Fig P31.10) the current in the solenoid changes as I = (5.00 A) sin (120t). Find the
Find the current through section PQ of length a = 65.0 cm in Figure P31.11. The circuit is located in a magnetic field whose magnitude varies with time according to the expression B = (1.00 x 10-3
A 30-turn circular coil of radius 4.00 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time
A long solenoid has n = 400 turns per meter and carries a current given by I = (30.0 A) (1 €“ e-1.60t). Inside the solenoid and coaxial with it is a coil that has a radius of 6.00 cm and
An instrument based on induced emf has been used to measure projectile speeds up to 6 km/s. A small magnet is imbedded in the projectile, as shown in Figure P31.14. The projectile passes through two
A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0° with the direction of the
When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude I max of the current without disconnecting the wire to shunt the current in a meter.
A toroid having a rectangular cross section (a = 2.00 cm by b = 3.00 cm) and inner radius R = 4.00 cm consists of 500 turns of wire that carries a sinusoidal current I = I max sin wt, with I max =
A piece of insulated wire is shaped into a figure 8, as in Figure P31.18. The radius of the upper circle is 5.00 cm and that of the lower circle is 9.00 cm. The wire has a uniform resistance per unit
An automobile has a vertical radio antenna 1.20 m long. The automobile travels at 65.0 km/h on a horizontal road where the Earth’s magnetic field is 50.0 /T directed toward the north and downward
Consider the arrangement shown in Figure P31.20. Assume that R = 6.00 Ω, ℓ = 1.20 m, and a uniform 2.50-T magnetic field is directed into the page. At what speed should the bar be moved
Figure P31.20 shows a top view of a bar that can slide without friction. The resistor is 6.00 Ω and a 2.50-T magnetic field is directed perpendicularly downward, into the paper. Let ℓ =
A conducting rod of length ℓ moves on two horizontal, frictionless rails, as shown in Figure P31.20. If a constant force of 1.00 N moves the bar at 2.00 m/s through a magnetic field B that is
Very large magnetic fields can be produced using a procedure called flux compression. A metallic cylindrical tube of radius R is placed coaxially in a long solenoid of somewhat larger radius. The
The homo polar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical
A flexible metallic wire with linear density 3.00 x 10-3 kg/m is stretched between two fixed clamps 64.0 cm apart and held under tension 267 N. A magnet is placed near the wire as shown in Figure
The square loop in Figure P31.26 is made of wires with total series resistance 10.0 (. It is placed in a uniform 0.100-T magnetic field directed perpendicularly into the plane of the paper. The loop,
A helicopter (Figure P31.27) has blades of length 3.00 m, extending out from a central hub and rotating at 2.00 rev/s. If the vertical component of the Earth€™s magnetic field is 50.0 /T,
Use Lenz€™s law to answer the following questions concerning the direction of induced currents.(a) What is the direction of the induced current in resistor R in Figure P31.28a when the bar
A rectangular coil with resistance R has N turns, each of length ℓ and width w as shown in Figure P31.29. The coil moves into a uniform magnetic field B with constant velocity v. What are the
In Figure P31.30, the bar magnet is moved toward the loop. Is Va - Vb positive, negative, or zero? Explain.
Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00-Ω resistor. The circuit also contains two metal rods having resistances of 10.0 Ω and15.0
For the situation shown in Figure P31.32, the magnetic field changes with time according to the expression B = (2.00t 3 - 4.00t 2 + 0.800)T, and r2 = 2R = 5.00 cm.(a) Calculate the magnitude and
A magnetic field directed into the page changes with time according to B = (0.030 0t + 2 1.40)T, where t is in seconds. The field has a circular cross section of radius R = 2.50 cm (Fig. P31.32).
A long solenoid with 1 000 turns per meter and radius 2.00 cm carries an oscillating current given by I = (5.00 A) sin (100,t). What is the electric field induced at a radius r = 1.00 cm from the
A coil of area 0.100 m2 is rotating at 60.0 rev/s with the axis of rotation perpendicular to a 0.200-T magnetic field (a) If the coil has 1 000 turns, what is the maximum emf generated in it? (b)
In a 250-turn automobile alternator, the magnetic flux in each turn is ǿB = (2.50 x 10-4 Wb) cos (wt), where w is the angular speed of the alternator. The alternator is geared to rotate three
A long solenoid, with its axis along the x axis, consists of 200 turns per meter of wire that carries a steady current of 15.0 A. A coil is formed by wrapping 30 turns of thin wire around a circular
A bar magnet is spun at constant angular speed w around an axis as shown in Figure P31.38. A stationary flat rectangular conducting loop surrounds the magnet, and at t = 0, the magnet is oriented as
A motor in normal operation carries a direct current of 0.850 A when connected to a 120-V power supply. The resistance of the motor windings is 11.8 (. While in normal operation, (a) what is the
A semicircular conductor of radius R = 0.250 m is rotated about the axis AC at a constant rate of 120 rev/min (Fig. P31.40). A uniform magnetic field in all of the lower half of the figure is
The rotating loop in an AC generator is a square 10.0 cm on a side. It is rotated at 60.0 Hz in a uniform field of 0.800 T. Calculate (a) The flux through the loop as a function of time, (b) The
Figure P31.42 represents an electromagnetic brake that uses eddy currents. An electromagnet hangs from a railroad car near one rail. To stop the car, a large current is sent through the coils of the
A conducting rectangular loop of mass M, resistance R, and dimensions w by ℓ falls from rest into a magnetic field B as shown in Figure P31.43. During the time interval before the top edge of
An electron moves through a uniform electric field E = (2.50i 2 5.00j) V/m and a uniform magnetic field B = (0.400k) T. Determine the acceleration of the electron when it has a velocity v = 10.0i m/s.
A proton moves through a uniform electric field given by E = 50.0j V/m and a uniform magnetic field B = (0.200i 2 0.300j 2 0.400k) T. Determine the acceleration of the proton when it has a velocity v
A steel guitar string vibrates (Figure 31.6). The component of magnetic field perpendicular to the area of a pickup coil nearby is given by B = 50.0 mT 2 (3.20 mT) sin (2, 523 t/s) The circular
Figure P31.47 is a graph of the induced emf versus time for a coil of N turns rotating with angular speed w in a uniform magnetic field directed perpendicular to the axis of rotation of the coil.
A technician wearing a brass bracelet enclosing area 0.005 00 m2 places her hand in a solenoid whose magnetic field is 5.00 T directed perpendicular to the plane of the bracelet. The electrical
Two infinitely long solenoids (seen in cross section) pass through a circuit as shown in Figure P31.49. The magnitude of B inside each is the same and is increasing at the rate of 100 T/s. What is
A conducting rod of length ℓ = 35.0 cm is free to slide on two parallel conducting bars as shown in Figure P31.50. Two resistors R1 = 2.00 Ω and R2 = 5.00 Ω are connected across the
Suppose you wrap wire onto the core from a roll of cellophane tape to make a coil. Describe how you can use a bar magnet to produce an induced voltage in the coil. What is the order of magnitude of
A bar of mass m, length d, and resistance R slides without friction in a horizontal plane, moving on parallel rails as shown in Figure P31.52. A battery that maintains a constant emf Є is
A particle with a mass of 2.00 x 10-16 kg and a charge of 30.0 nC starts from rest, is accelerated by a strong electric field, and is fired from a small source inside a region of uniform constant
An induction furnace uses electromagnetic induction to produce eddy currents in a conductor, thereby raising the conductor’s temperature. Commercial units operate at frequencies ranging from 60 Hz

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