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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Consider two ideal inductors L1 and L2 that have zero internal resistance and are far apart, so that their magnetic fields do not influence each other. (a) Assuming these inductors are connected in
Calculate the energy associated with the magnetic field of a 200-turn solenoid in which a current of 1.75 A produces a flux of 3.70 x 10-4 Wb in each turn.
The magnetic field inside a superconducting solenoid is 4.50 T. The solenoid has an inner diameter of 6.20 cm and a length of 26.0 cm. Determine (a) The magnetic energy density in the field and
An air-core solenoid with 68 turns is 8.00 cm long and has a diameter of 1.20 cm. How much energy is stored in its magnetic field when it carries a current of 0.770 A?
At t = 0, an emf of 500 V is applied to a coil that has an inductance of 0.800 H and a resistance of 30.0 Ω. (a) Find the energy stored in the magnetic field when the current reaches half its
On a clear day at a certain location, a 100-V/m vertical electric field exists near the Earth’s surface. At the same place, the Earth’s magnetic field has a magnitude of 0.500 x 10-4 T. Compute
Complete the calculation in Example 32.4 by proving that
An RL circuit in which L = 4.00 H and R = 5.00 Ω is connected to a 22.0-V battery at t = 0. (a) What energy is stored in the inductor when the current is 0.500 A? (b) At what rate is energy
A 10.0-V battery, a 5.00-Ω. resistor, and a 10.0-H inductor are connected in series. After the current in the circuit has reached its maximum value, calculate (a) The power being supplied by
A uniform electric field of magnitude 680 kV/m throughout a cylindrical volume results in a total energy of 3.40 μJ. What magnetic field over this same region stores the same total energy?
Assume that the magnitude of the magnetic field outside a sphere of radius R is B = B0(R/r)2, where B0 is a constant. Determine the total energy stored in the magnetic field outside the sphere and
Two coils are close to each other. The first coil carries a time varying current given by I (t) = (5.00 A) e-0.025 0t sin (377t). At t = 0.800 s, the emf measured across the second coil is -3.20 V.
Two coils, held in fixed positions, have a mutual inductance of 100 μH. What is the peak voltage in one when a sinusoidal current given by I (t) = (10.0 A) sin (1 000t) is in the other coil?
An emf of 96.0 mV is induced in the windings of a coil when the current in a nearby coil is increasing at the rate of 1.20 A/s. What is the mutual inductance of the two coils?
On a printed circuit board, a relatively long straight conductor and a conducting rectangular loop lie in the same plane, as shown in Figure P31.9. Taking h = 0.400 mm, w = 1.30 mm, and L = 2.70 mm,
Two solenoids A and B, spaced close to each other and sharing the same cylindrical axis, have 400 and 700 turns, respectively. A current of 3.50 A in coil A produces an average flux of 300 μ Wb
A large coil of radius R1 and having N1 turns is coaxial with a small coil of radius R2 and having N2 turns. The centers of the coils are separated by a distance x that is much larger than R1 and R2.
Two inductors having self-inductances L1 and L2 are connected in parallel as shown in Figure P32.45a. The mutual inductance between the two inductors is M. Determine the equivalent self-inductance
A 1.00μF capacitor is charged by a 40.0-V power supply. The fully charged capacitor is then discharged through a 10.0-mH inductor. Find the maximum current in the resulting oscillations.
An LC circuit consists of a 20.0-mH inductor and a 0.500- μF capacitor. If the maximum instantaneous current is 0.100 A, what is the greatest potential difference across the capacitor?
In the circuit of Figure P32.48, the battery emf is 50.0 V, the resistance is 250 Ω, and the capacitance is 0.500 μF. The switch S is closed for a long time and no voltage is measured across
A fixed inductance L = 1.05 'H is used in series with a variable capacitor in the tuning section of a radiotelephone on a ship. What capacitance tunes the circuit to the signal from transmitter
Calculate the inductance of an LC circuit that oscillates at 120 Hz when the capacitance is 8.00 μF.
An LC circuit like the one in Figure 32.16 contains an 82.0-mH inductor and a 17.0-μF capacitor that initially carries a 180-μC charge. The switch is open for t < 0 and then closed at t =
The switch in Figure P32.52 is connected to point a for a long time. After the switch is thrown to point b, what are(a) The frequency of oscillation of the LC circuit,(b) The maximum charge that
An LC circuit like that in Figure 32.16 consists of a 3.30-H inductor and an 840-pF capacitor, initially carrying a 105-μC charge. The switch is open for t < 0 and then closed at t = 0. Compute
In Figure 32.21, let R = 7.60 Ω, L = 2.20 mH, and C = 1.80 μF. (a) Calculate the frequency of the damped oscillation of the circuit. (b) What is the critical resistance?
Consider an LC circuit in which L = 500 mH and C = 0.100 μF. (a) What is the resonance frequency 10? (b) If a resistance of 1.00 k. is introduced into this circuit, what is the frequency of
Show that Equation 32.28 in the text is Kirchhoff’s loop rule as applied to the circuit in Figure 32.21.
The energy of an RLC circuit decreases by 1.00% during each oscillation when R = 2.00 Ω. If this resistance is removed, the resulting LC circuit oscillates at a frequency of 1.00 kHz. Find the
Electrical oscillations are initiated in a series circuit containing a capacitance C, inductance L, and resistance R. (a) If R
This problem extends the reasoning of Section 26.4, Problem 26.37, Example 30.6, and Section 32.3. (a) Consider a capacitor with vacuum between its large, closely spaced, and oppositely charged
Initially, the capacitor in a series LC circuit is charged. A switch is closed at t = 0, allowing the capacitor to discharge, and at time t the energy stored in the capacitor is one fourth of its
A 1.00-mH inductor and a 1.00-μF capacitor are connected in series. The current in the circuit is described by I = 20.0t, where t is in seconds and I is in amperes. The capacitor initially has
An inductor having inductance L and a capacitor having capacitance C are connected in series. The current in the circuit increases linearly in time as described by I = Kt, where K is a constant. The
A capacitor in a series LC circuit has an initial charge Q and is being discharged. Find, in terms of L and C, the flux through each of the N turns in the coil, when the charge on the capacitor is
The toroid in Figure P32.64 consists of N turns and has a rectangular cross section. Its inner and outer radii are a and b, respectively.(a) Show that the inductance of the toroid is(b) Using this
(a) A flat circular coil does not really produce a uniform magnetic field in the area it encloses, but estimate the self-inductance of a flat, compact circular coil, with radius R and N turns, by
A soft iron rod ('m = 800'0) is used as the core of a solenoid. The rod has a diameter of 24.0 mm and is 10.0 cm long. A 10.0-m piece of 22-gauge copper wire (diameter = 0.644 mm) is wrapped around
A wire of nonmagnetic material, with radius R, carries current uniformly distributed over its cross section. The total current carried by the wire is I. Show that the magnetic energy per unit length
An 820-turn wire coil of resistance 24.0 Ω is placed around a 12 500-turn solenoid 7.00 cm long, as shown in Figure P32.68. Both coil and solenoid have cross-sectional areas of 1.00 x 10-4
At t = 0, the open switch in Figure P32.69 is closed. By using Kirchhoff€™s rules for the instantaneous currents and voltages in this two-loop circuit, show that the current in the inductor
In Figure P32.69 take Є = 6.00 V, R1 = 5.00 Ω, and R2 = 1.00 Ω. The inductor has negligible resistance. When the switch is opened after having been closed for a long time, the current
In Figure P32.71, the switch is closed for t (b) Make freehand graphs of the currents in R1 and in R2 as a function of time, treating the steady-state directions as positive. Show values before
The open switch in Figure P32.72 is closed at t = 0. Before the switch is closed, the capacitor is uncharged, and all currents are zero. Determine the currents in L, C, and R and the potential
To prevent damage from arcing in an electric motor, a discharge resistor is sometimes placed in parallel with the armature. If the motor is suddenly unplugged while running, this resistor limits the
An air-core solenoid 0.500 m in length contains 1 000 turns and has a cross-sectional area of 1.00 cm2. (a) Ignoring end effects, find the self-inductance. (b) A secondary winding wrapped around
The lead-in wires from a television antenna are often constructed in the form of two parallel wires (Fig. P32.75)(a) Why does this configuration of conductors have an inductance?(b) What constitutes
The resistance of a superconductor in an experiment carried out by S. C. Collins between 1955 and 1958, a current was maintained in a superconducting lead ring for 2.50 yr with no observed loss. If
A novel method of storing energy has been proposed. A huge underground superconducting coil, 1.00 km in diameter, would be fabricated. It would carry a maximum current of 50.0 kA through each winding
Superconducting power transmission the use of superconductors has been proposed for power transmission lines. A single coaxial cable (Fig P32.78) could carry 1.00 x 103 MW (the output of a large
The Meissner effect Compare this problem with Problem 65 in Chapter 26, on the force attracting a perfect dielectric into a strong electric field. A fundamental property of a Type I superconducting
Excess electrons are placed on a small lead sphere with mass 8.00 g so that its net charge is - 3.20 X 10-9 C. (a) Find the number of excess electrons on the sphere. (b) How many excess electrons are
Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about 20,000 C/s; this
Estimate how many electrons there are in your body. Make any assumptions you feel are necessary, but clearly state what they are. (Hint: Most of the atoms in your body have equal numbers of
Particles in a Gold Ring. You have a pure (24-karat) gold ring with mass 17.7 g. Gold has an atomic mass of 197 g/mol and an atomic number of 79. (a) How many protons are in the ring, and what is
An average human weighs about 650 N. If two such generic humans each carried 1.0 coulomb of excess charge, one positive and one negative, how far apart would they have to be for the electric
Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is4.57 X 10-2 ' N?
Two small plastic spheres are given positive electrical charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere? (a) If the two
Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a) How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 g/mol, and its atomic number
Two very small 8.55-g spheres, 15.0 cm apart from center to center, are charged by adding equal numbers of electrons to each of them. Disregarding all other forces, how many electrons would you have
(a) Assuming that only gravity is acting on it, how far does an electron have to be from a proton so that its acceleration is !he same as that of a freely falling object at the earth's surface? (b)
In an experiment in space, one proton is held fixed and another proton is released from rest a distance of 2.50 mm away. (a) What is the initial acceleration of the proton after it is released? (b)
A negative charge -0.550µC exerts an upward 0.200-N force on an unknown charge 0.300 m directly below it. (a) What is the unknown charge (magnitude and sign)?(b) What are the magnitude and direction
Three point charges are arranged on a line. Charge q3 = + 5.00 nC and is at the origin. Charge q2 = - 3.00 nC and is at x = +4.00cm. Charge q1 is at x = +2.00cm. What is q1 (magnitude and sign) if
In Example 21.4, suppose the point charge on the y-axis at y = -0.30 m has negative charge -2.0, µC, and the other charges remain the same. Find the magnitude and direction of the net force on Q.
In Example 21.3, calculate the net force on charge q1.
In Example 21.4, what is the net force (magnitude and direction) on charge q1 exerted by the other two charges?
Three point charges are arranged along the x-axis. Charge q1 = +3.00µC is at the origin, and charge q2 = -5.00µC is at x = 0.200 m. Charge q, = - 8.00 µC. Where is q3 located if the net force on
Repeat Exercise 21.17, for q3 = +8.00µC.
Two point charges are located on the y-axis as follows: charge q1 = -1.50 nC at y = -0.600m, and charge q2 = +3.20 nC at the origin (y = 0). What is the total force (magnitude and direction) exerted
Two point charges are placed on the x-axis as follows: Charge q1 = +4.00 nC is located at x = 0.200 m, and charge q2 = +5.00 nC is at x = -0.300 m. What are the magnitude and direction of the total
A positive point charge q is placed on the +y-axis at y = a, and a negative point charge –q is placed on the -y-axis at y = -a. A negative point charge - Q is located at some point on the + x-axis.
Two positive point charges q are placed on the y-axis at y = a and y = -a. A negative point charge -Q is located at some point on the +x-axis. (a) In a free-body diagram, show the forces that act on
Four identical charges Q are placed at the corners of a square of side L. (a) In a free-body diagram, show all of the forces that act on one of the charges. (b) Find the magnitude and direction of
Two charges, one of 2.50 µC and the other of - 3.50 µC, are placed on the x-axis, one at the origin and the other at x = 0.600 m, as shown in Fig. 21.36. Find the position on the x-axis
A proton is placed in a uniform electric field of 2.75 X103 N/C. Calculate: (a) The magnitude of the electric force felt by the proton;(b) The proton's acceleration; (c) The proton's speed after 1.00
A particle has charge - 3.00 nC. (a) Find the magnitude and direction of the electric field due to this particle at a point 0.250 m directly above it. (b) At what distance from this particle does its
A proton is traveling horizontally to the right at 4.50 X 106 m/s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of
An electron is released from rest in a uniform electric field. The electron accelerates vertically upward, traveling 4.50 m in the first 3.00 µs after it is released. (a) What are the magnitude and
(a) What must the charge (sign and magnitude) of a 1.45-g particle be for it to remain stationary when placed in a downward directed electric field of magnitude 650 N/C? (b) What is the magnitude of
(a) What is the electric field of an iron nucleus at a distance of 6.00 X 10-10 m from the nucleus? The atomic number of iron is 26. Assume that the nucleus may be treated as a point charge. (b) What
Two point charges are separated by 25.0 cm (Fig. 21.37). Find the net electric field these charges produce at(a) point A and(b) point B.(c) What would be the magnitude and direction of the electric
Electric Field of the Earth The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. (a) What magnitude and
An electron is projected with an initial speed U0 = 1.60 X 106 m/s into the uniform field between the parallel plates in Fig. 21.38. Assume that the field between the plates is uniform and directed
Point charge q1 = -5.00 NC is at the origin and point charge q2 = +3.00 NC is on the x-axis at x = 3.00 cm. Point P is on the y-axis at Y = 4.00 cm. (a) Calculate the electric fields E1 and E2 at
In Exercise 21.33, what is the speed of the electron as it emerges from the field?
(a) Calculate the magnitude and direction (relative to the + x-axis) of the electric field in Example 21.6. (b) A - 2.5-nC point charge is placed at the point P in Fig. 21.19. Find the magnitude and
(a) For the electron in Examples 21.7 and 21.8, compare the weight of the electron to the magnitude of the electric force on the electron. Is it appropriate to ignore the gravitational force on the
A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the
A point charge is at the origin. With this point charge as the source point, what is the uo it vector r in the direction of (a) The field point at x = 0, y = -1.35 m; (b) The field point at x = 12.0
A +8.75-µC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-µC point charge by a light, non conducting 2.50-cm wire. A uniform electric field of magnitude 1.85 X
(a) An electron is moving east in a uniform electric field of 1.50 N/c directed to the west. At point A, the velocity of the electron is 4.50 X l05 m/s toward the east. What is the speed of the
Electric Field in the Nucleus Protons in the nucleus are of the order of 10-15 m (1 fin) apart. (a) What is the magnitude of the electric field produced by a proton at a distance of 1.50 fm from it?
Two positive point charges q are placed on the x-axis, one at x = a and one at x = -a. (a) Find the magnitude and direction of the electric field at x = 0. (b) Derive an expression for the electric
Two particles having charges q1 = 0.500 nC and q2 = 8.00 nC are separated by a distance of 1.20 m. At what point along the line connecting the two charges is the total electric field due to the two
A + 2.00-nC point charge is at the origin, and a second - 5.00 -nC point charge is on the x-axis at x = 0.800 m. (a) Find the electric field (magnitude and direction) at each of the following points
Repeat Exercise 21.44, but now let q1 = -4.00 nC.
Three negative point charges lie along a line as shown in Fig. 21.40. Find the magnitude and direction of the electric field this combination of charges produces at point P, which lies 6.00 cm. from
A positive point charge q is placed at x = a, and a negative point charge -q is placed at x = -a. (a) Find the magnitude and direction of the electric field at x = 0. (b) Derive an expression for the

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