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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

The wire shown in Fig is infinitely long and carries a current L Calculate the magnitude and direction of the magnetic field that this current produces at point P.
A 0.25 kg skeet (clay target) is fired at an angle of 30o to the horizon with a speed of 25m/s (Fig. 7-45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling
(a) For the coaxial cable of Exercise28.37, derive an expression for the magnitude of the magnetic field at points inside the central solid conductor (r < a). Compare your result when r = a to the
The electric field of an infinite line of positive charge is directed radically outward from the wire and can be calculated using Gauss's law for the electric field (see Example 22.6 in Section
A conductor is made in the form of a hollow cylinder with inner and outer radii a and b, respectively. It carries a current 1 uniformly distributed over its cross section. Derive expressions for the
Knowing Magnetic Fields Inside and Out. You are given a hollow copper cylinder with inner radius a and outer radius 3a. The cylinder's length is 200a and its electrical resistance to current flowing
A circular loop has radius R and carries current I2 in a clockwise direction (Fig). The center of the loop is a distance D above a long, straight wire. What are the magnitude and direction of the
A long straight solid cylinder oriented with its axis in the z-direction, carries a current whose current density is 1. The current density, although symmetrical about the cylinder axis, is not
A long, straight, solid cy1inder, oriented with its axis in the z-direction, carries a current whose current density is J. The current density, although symmetrical about the cylinder axis, is not
Integrate Bx as given in Eq. (28.15) from -∞ to +∞; that is, calculate f+∞ -∞ Bx dx Explain the significance of your result.
In a region of space where there are no conduction or displacement currents, it is impossible to have a uniform magnetic field that abruptly drops to zero. To prove this statement, use the method of
(a) What are the magnitude and direction of the magnetic field a distance a below the current sheet?(b) What are the magnitude and direction of the magnetic field a distance a above the current sheet?
Long, straight conductors with square cross section, each carrying current I, are laid side by side to form an infinite current sheet with current directed out of the plane of the page (Fig. 28.65).A
A piece of iron bas magnetization M = 6.50 X 104 A/m. Find the average magnetic dipole moment per atom in this piece of iron. Express your answer both in A • m2 and in Bohr magnet on s. The density
(a) In Section 27.7 we discussed how a magnetic dipole, such as a current loop or a magnetized object, can be attracted or repelled by a permanent magnet. Use this to explain why either pole of a
Two long, straight conducting wires with linear mass density A are suspended from cords so that they are each horizontal, parallel to each other, and a distance d apart. The back ends of the wires
A wide, long, insulating belt has a uniform positive charge per unit area u on its upper surface. Rollers at each end move the belt to the right at a constant speed u. Calculate the magnitude and
A Charged Dielectric Disk. A thin disk of dielectric material with radius a has a total charge + Q distributed uniformly over its surface. It rotates n times per second about an axis perpendicular to
A wire in the shape of semicircle with radius a is oriented in the yz-plane with its center of curvature at the origin (Fig. 28.67). If the current in the wire is I, calculate the magnetic-field
If the current in a 180-mH coil changes steadily from 25.0 A to 10.0 A in 350 ms, what is the magnitude of the induced emf?
What is the inductance of a coil if the coil produces an emf of 2.50 V when the current in it changes from -28.0mA to +31.0 mA in 12.0 ms?
What is the inductance L of a 0.60-m-long air-filled coil 2.9 cm in diameter containing 10,000 loops?
How many turns of wire would be required to make a 130-mH inductance out of a 30.0-cm-long air-filled coil with a diameter of 5.2 cm?
An air-filled cylindrical inductor has 2800 turns, and it is 2.5cm in diameter and 28.2 cm long. (a) What is its inductance? (b) How many turns would you need to generate the same inductance if the
A coil has 2.25-Ω resistance and 440-mH inductance. If the current is 3.00 A and is increased at a rate of 3.50 A/s, what is the potential difference across the coil at this moment?
A long thin solenoid of length l and cross-sectional area A contains N1 closely packed turns of wire. Wrapped tightly around it is an insulated coil of N2 turns, Fig.21-52. Assume all the flux from
The wire of a tightly wound solenoid is unwound and used to make another tightly wound solenoid of twice the diameter. By what factor does the inductance change?
The magnetic flux through a coil of wire containing two loops changes from -50 Wb to +38Wb in 0.42 s. What is the emf induced in the coil?
The rectangular loop shown in Fig. 21-46 is pushed into the magnetic field which points inward. In what direction is the induced current?
The north pole of the magnet in Fig. 21-47 is being inserted into the coil. In which direction is the induced current flowing through the resistor R?
A 9.6-cm-diameter circular loop of wire is in a 1.10-T magnetic field. The loop is removed from the field in 0.15 s. What is the average induced emf?
A 12.0-cm-diameter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average
A 10.2-cm-diameter wire coil is initially oriented so that its plane is perpendicular to a magnetic field of 0.63 T pointing up. During the course of 0.15 s. the field is changed to one of 0.25 T
A 15-cm-diameter circular loop of wire is placed in a 0.50-T magnetic field. (a) When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? (b)
(a) If the resistance of the resistor in Fig. 21-48 is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop?(b) What would it be if the
What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. 21-49?
If the solenoid in Fig. 21-50 is being pulled away from the loop shown, in what direction is the induced current in the loop?
The magnetic field perpendicular to a circular wire loop 12.0 cm in diameter is changed from +0.52 T to -0.45 T in 180 ms, where +means the field points away from an observer and –toward the
The moving rod in Fig.21-12 is 12.0 long and is pulled at a speed of 15.0 cm/s. If the magnetic field is 0.800 T, calculate (a) The emf developed, and (b) The electric field felt by electrons in the
A circular loop in the plane of the paper lies in a 0.75-T magnetic field pointing into the paper. If the loop’s diameter changes from 20.0 cm to 6.0 cm in 0.50 s (a) What is the direction of the
The moving rod in Fig 21-12 is 13.2 cm long and generates an emf of 120 mV while moving in a 0.90-T magnetic field. (a) What is its speed?(b) What is the electric field in the rod?
A 500-turn solenoid, 25 cm long, has a diameter of 2.5 cm. A 10-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increased uniformly from 0 to 5.0A in 0.60
In Fig 21-12, the rod moves with a speed of 1.6 m/s, is 30.0 cm long, and has a resistance of 2.5 Ω. The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is 25.0 Ω at
A 22.0 cm diameter coil consists of 20 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to plane of the coil, changes at a rare of 8.65 x 103 T/s Determine
The magnetic field perpendicular to a single 13.2-cm-diameter circular loop of copper wire decreased uniformly from 0.750 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a
A simple generator is used to generate a peak output voltage of 24.0 V. The square armature consists of windings that are 6.0 cm on a side and rotates in a field of 0.420 T at a rate of 60.0 rev/s,
The generator of a car idling at 1100 rpm produces 12.4V. What will the output be at a rotation speed of 2500 rpm assuming nothing else changes?
Show that rms output of and ac generator is V rms = NABw/√2, where w = 2πf .
A simple generator has a 320-loop square coil 21.0 cm on a side. How fast must it turn in a 0.650 T field to produce a 120-V peak output?
A 450-loop circular armature coil with a diameter of 8.0 cm rotates at120 rev/s in a uniform magnetic field of strength 0.55 T(a) What is the rms voltage output of the generator? (b) What would you
A generator rotates at 85.Hz in a magnetic field of 0.030 T. It has 1000 turns and produces an rms voltage of 150 V and rms current of 70.0 A.(a) What is the peak current produced?(b) What is the
A motor has an armature resistance of 3.25 Ω. If it draws 8.20 A when running at full speed and connected to a 120-V line, how large is the back emf?
The back emf in a motor is 72 V when operating at 1800 rpm. What would be the back emf at 2500 rpm if the magnetic field is unchanged?
The back emf in a motor is 95 V when the motor is operating at 1000 rpm. How would you change the motor’s magnetic field if you wanted to reduce the back emf to 65 V when the motor was running at
What will be the current in the motor of Example 21-9 if the load causes it to run at half speed?
A transformer is designed to change 120 V into 10,000 V and there are 164 turns in the primary coil. How many turns are in the secondary coil?
A transformer has 320 turns in the primary coil and 120 in the secondary coil. What kind of transformer is this, and by what factor does if changes the voltage? By what factor does if change the
A step-up transformer increases 25 V to 120 V. what is the current in the secondary coil as compared to the primary coil?
Neon signs require 12 kV for their operation. To operate from a 240-V linc, what must be the ratio of secondary to primary turns of the transformer? What would the voltage primary turns of the
A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 7.5 A to the train. (a) What voltage is present across the tracks?(b) Is the transformer step-up or step-down?
The output voltage of a 95-W transformer is 12 V, and the input current is 22 A.(a) Is this a step-up or a step-down transformer?(b) By what factor is the voltage multiplied?
A transformer has 330 primary turns and 1340 secondary turns. The input voltage is 120 V and the output current is 15.0 A. What are the output voltage and input current?
If 30 MW of power at 45 k V (rms) arrives at a town from a generator via 4.0-Ω transmission lines, calculate. (a) The emf at the generator end of the lines, and. (b) The fraction of the
65kW is to arrive at a town over two 0.100- Ω lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at
The magnetic field inside and air-filled solenoid 36 cm long and 2.0 cm in diameter is 0.80 T. Approximately how much energy is stored in this field?
At a given instant the current through an inductor is 50.0mA and is increased at the rate of 115 mA/s. What is the initial energy stored in the inductor if the inductance is known to be 60.0 mH, and
Assuming the Earth’s magnetic field averages about 0.50 x 10-4 T near the surface of the Earth, estimate the total energy stored in this field in the first 10 km above the earth’s surface.
Determine ΔI /Δt at t = 0 (when the battery is connected) for the LR circuit of Fig.21-33 and show that if I continued to increase at this rate, it would reach its maximum value in
After how many time constants does the current in Fig 21-33 reach within? (a) 10%,(b) 1.0%,(c) 0.1% of its maximum value?
Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1uses wire that is half as thick as solenoid 2. (a) What is the ratio of their inductances?(b)What is
What is the reactance of a 7.20-μF capacitor at a frequency of? (a) 60.0 Hz, (b)1.00 MHz?
At what frequency will a 22.0-mH inductor have a reactance of 660 Ω?
At what frequency will a 2.40-μF capacitor have a reactance of 6.70 kΩ?
Plot a graph of the reactance of a 1.0-μF capacitor as a function of frequency from 100 to 10,000 Hz.
Plot a graph of the reactance of a 1.0-mH inductor as a function of frequency from 100 to 10,000 Hz.
Calculate the reactance of, and rms current in, a 160-mH radio coil connected to a 240-V (rms) 10.0-kHz ac line. Ignore resistance.
An inductance coil operates at 240 V and 60.0 Hz. It draws 12.8 A. What is the coil’s inductance?
(a) What is the reactance of a well-insulated 0.030-μF capacitor connected to a 2.0-kV (rms)720-Hz line? (b) What will be the peak value of the current?
A 30-kΩ resistor is in series with a 45-mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is. (a) 50 Hz, and. (b) 3.0 x 104 Hz.
A 3.5-kΩ resistor and a 4.0-μF capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is. (a) 60 Hz, and (b) 60,000 Hz.
For a 120-V rms current of 70 mA passing through the human body for 1.0 s could be lethal. What must be the impedance of the body for this to occur?
What is the resistance of coil if its impedance is 235 Ω and its reactance is 135 Ω?
What are the total impedance, phase angle, and rms current in and LRC circuit connected to a 10.0-kHz, 725-V (rms) source if L = 22.0 mH, R = 8.70 kΩ, and C = 3250 pF?
A 2.5-kΩ resistor in series with a 420-mH inductor is driven by an ac power supply. At what frequency is the impedance double that of the impedance at 60 Hz?
(a) What is the rms current in an RL circuit when a 60.0-Hz 120-V rms ac voltage is applied, where R = 1.80 kΩ, and L = 350 mH? (b) What is the phase angle between voltage and current? (c)
(a) What is the rms current in an RC circuit if R = 8.80 kΩ, C = 1.80 μF, and the rms applied voltage is 120 V at 60.0 Hz? (b) What is the phase angle between voltage and current? (c)
A 3500-pF capacitor is connected to a 55.0-μH coil of resistance 3.00 Ω. What is the resonant frequency of this circuit?
The variable capacitor in the tuner of an AM radio has a capacitance of 2800 pF when the radio is tuned to a station at 580 kHz. (a) What must be the capacitance for a station at 1600 kHz?(b) What is
An LRC circuit has L = 14.8 mH and R =4.40 Ω. (a) What value must C have to produce resonance at 3600 Hz? (b) What will be the maximum current at resonance if the peak external voltage is 150
Suppose you are looking at two currents loops in the plane of the page as shown in Fig. 21-53. When switch S is thrown in the left-hand side coil,(a) What is the direction of the induced current in
A square loop 24.0 cm on a side has a resistance of 5.20 Ω. It is initially in a 0.665-T magnetic field, with its plane perpendicular to B, but is removed from the field in 40.0 ms. Calculate
A high-intensity desk lamp is rated at 45 W but requires only 12 V. It contains a transformer that converts 120-V household voltage.(a) Is the transformer step-up or step-down?(b) What is the current
Power is generated at 24 kV at a generated plant located 118 km from a town that requires 50 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of 0.10
The primary windings of a transformer which has an 80% efficiency are connected to 110-V ac. The secondary windings are connected across a 2.4-Ω, 75-W lightbulb, (a) Calculate the current
A pair of power transmission lines each have a 0.80-Ω resistance is 42 kV, calculate. (a) The voltage at the other end, (b) The power input, (c) Power loss in the lines, and. (d) The
Two resistanceless rails rest 32 cm apart on a 6.0o ramp. They are joined at the bottom by a 0.60-Ω resistor. At the top a copper bar of mass 0.040 kg (ignore its resistance) is laid across the
Show that the power loss in transmission lines PL, is given by PL = (PT)2 RL/V2.Where PT is the power transmitted to the user, V is the delivered voltage, and RL is the resistance of the power lines.
A coil with 150 turns, a radius of 5.0 cm, and a resistance of 12Ω surrounds a solenoid with 230 turns/cm and a radius of 4.5 cm; see Fig 21-54. The current in the solenoid changes at a
A certain electronic device needs to be protected against sudden surges in current. In particular, after the power is turned on the current should rise no more than 7.5mA in the first 120μs. The
A 25-turn 12.5 cm-diameter coil is placed between the pole pieces of an electromagnet. When the magnet is turned on, the flux through the coil changes, inducing and emf at what rate (in T/s) must the

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