Will a nail be attracted to either pole of a magnet? Explain what is happening inside the nail when it is placed near the magnet.
> A wire carries a 7.00 - A current along the x - axis, and another wire carries a 6.00 - A current along the y - axis, as shown in Figure P19.51. What is the magnetic field at point P, located at x = 4.00 m, y = 3.00 m? Figure P19.51:
> Two long, parallel wires carry currents of I1 = 3.00 A and I2 = 5.00 A in the direction indicated in Figure P19.50. (a) Find the magnitude and direction of the magnetic field at a point midway between the wires (d = 20.0 cm). (b) Find the magnitude and d
> Four long, parallel conductors carry equal currents of I = 5.00 A. Figure P19.49 is an end view of the conductors. The direction of the current is into the page at points A and B (indicated by the crosses) and out of the page at C and D (indicated by the
> The two wires shown in Figure P19.48 are separated by d = 10.0 cm and carry currents of I = 5.00 A in opposite directions. Find the magnitude and direction of the net magnetic field (a) At a point midway between the wires; (b) At point P1, 10.0 cm to the
> A cardiac pacemaker can be affected by a static magnetic field as small as 1.7 mT. How close can a pacemaker wearer come to a long, straight wire carrying 20 A?
> In 1962 measurements of the magnetic field of a large tornado were made at the Geophysical Observatory in Tulsa, Oklahoma. If the magnitude of the tornado’s field was B = 1.50 x 10-8 T pointing north when the tornado was 9.00 km east of the observatory,
> Neurons in our bodies carry weak currents that produce detectable magnetic fields. A technique called magne-toencephalography, or MEG, is used to study electrical activity in the brain using this concept. This technique is capable of detecting magnetic f
> A long, straight wire going through the origin is carrying a current of 3.00 A in the positive z - direction (Fig. P19.44). At a point a distance r = 1.20 m from the origin on the positive x - axis, find the (a) Magnitude and (b) Direction of the magneti
> A charged particle moves in a straight line through a region of space. Which of the following answers must be true? (Assume any other fields are negligible.) The magnetic field (a) Has a magnitude of zero (b) Has a zero component perpendicular to the par
> A lightning bolt may carry a current of 1.00 x 104 A for a short time. What is the resulting magnetic field 1.00 x 102 m from the bolt? Suppose the bolt extends far above and below the point of observation.
> A rectangular loop has dimensions 0.500 m by 0.300 m. The loop is hinged along the x - axis and lies in the xy - plane (Fig. P19.42). A uniform magnetic field of 1.50 T is directed at an angle of 40.0° with respect to the positive y - axis and
> A long piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carries a 3.40 - A current, and is placed in a vertical magnetic field with a magn
> The orientation of small satellites is often controlled using torque from current - carrying coils in Earth’s magnetic field. Suppose a multi-turn coil has a cross - sectional area of 6.36 x 10-4 m2, dissipates 0.200 W of electrical power from a 5.00 - V
> A 6.00 - turn circular coil of wire is centered on the origin in the xy - plane. The coil has radius r = 0.200 m and carries a counterclockwise current I = 1.60 A (Fig. P19.39). (a) Calculate the magnitude of the coil’s magnetic moment.
> A current - carrying rectangular wire loop with width a = 0.120 m and length b = 0.200 m is in the xy - plane, supported by a non-conducting, frictionless axle of negligible weight. A current of I = 3.00 A travels counterclockwise in the circuit (Fig. P1
> An eight - turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (Fig. P19.37). The coil lies in the plane of the page and carries a clockwise current of 6.00 A. If the coil is in a uniform magnetic field of 2.0
> A current of 17.0 mA is maintained in a single circular loop with a circumference of 2.00 m. A magnetic field of 0.800 T is directed parallel to the plane of the loop. What is the magnitude of the torque exerted by the magnetic field on the loop?
> A wire is formed into a circle having a diameter of 10.0 cm and is placed in a uniform magnetic field of 3.00 mT. The wire carries a current of 5.00 A. Find the maximum torque on the wire.
> A horizontal power line of length 58 m carries a current of 2.2 kA as shown in Figure P19.34. Earth’s magnetic field at this location has a magnitude equal to 5.0 x 10-5 T and makes an angle of 65° with the power line. Find t
> If, in Figure 19.28, I1 = 2A and I2 = 6A, which of the following is true? (Note that F2 represents the magnitude of the force on wire 2.) (a) F1 = 3F2 (b) F1 = F2 (c) F1 = F2/3 Figure 19.28:
> In Figure P19.33, the cube is 40.0 cm on each edge. Four straight segments of wire—ab, bc, cd, and da — form a closed loop that carries a current I = 5.00 A in the direction shown. A uniform magnetic field of magnitude
> A metal rod of mass m carrying a current I glides on two horizontal rails a distance d apart. If the coefficient of kinetic friction between the rod and rails is μk, what vertical magnetic field is required to keep the rod moving at a constant speed?
> Consider the system pictured in Figure P19.31. A 15 - cm length of conductor of mass 15 g, free to move vertically, is placed between two thin, vertical conductors, and a uniform magnetic field acts perpendicular to the page. When a 5.0 - A current is di
> Mass m = 1.00 kg is suspended vertically at rest by an insulating string connected to a circuit partially immersed in a magnetic field as in Figure P19.30. The magnetic field has magnitude Bin = 2.00 T and the length â„“ = 0.500 m. (a) Fi
> A wire with a mass of 1.00 g/cm is placed on a horizontal surface with a coefficient of friction of 0.200. The wire carries a current of 1.50 A eastward and moves horizontally to the north. What are the magnitude and the direction of the smallest vertica
> At a certain location, Earth has a magnetic field of 0.60 x 10-4 T, pointing 75° below the horizontal in a north–south plane. A 10.0 - m - long straight wire carries a 15 - A current. (a) If the current is directed horizontally toward the east, what are
> A wire carries a current of 10.0 A in a direction that makes an angle of 30.0° with the direction of a magnetic field of strength 0.300 T. Find the magnetic force on a 5.00 - m length of the wire.
> A wire having a mass per unit length of 0.500 g/cm carries a 2.00 - A current horizontally to the south. What are the direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward?
> In Figure P19.3, assume in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic field that will produce the magnetic force shown. Figure
> A straight wire carrying a 3.0 - A current is placed in a uniform magnetic field of magnitude 0.28 T directed perpendicular to the wire. (a) Find the magnitude of the magnetic force on a section of the wire having a length of 14 cm. (b) Explain why you c
> Which of the following actions would double the magnitude of the magnetic force per unit length between two parallel current - carrying wires? Choose all correct answers. (a) Double one of the currents. (b) Double the distance between them. (c) Reduce th
> A current I = 15 A is directed along the positive x - axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.12 N/m acts on the conductor in the negative y - direction. Calculate the magnitude and direction of the magnetic fiel
> In Figure P19.2, assume in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic force acting on the wire. Figure P19.2:
> A particle passes through a mass spectrometer as illustrated in Figure P19.15. The electric field between the plates of the velocity selector has a magnitude of 8250 V/m, and the magnetic fields in both the velocity selector and the deflection chamber ha
> A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference ΔV. Each of the particles enters a uniform magnetic field B(, with its velocity
> A proton is at rest at the plane vertical boundary of a region containing a uniform vertical magnetic field B (Fig. P19.19). An alpha particle moving horizontally makes a head - on elastic collision with the proton. Immediately after the collision, both
> Two long, straight wires cross each other at right angles, and each carries the same current as in Figure CQ19.18. Which of the following statements are true regarding the total magnetic field at the various points due to the two wires? (There may be mor
> Jupiter’s magnetic field occupies a volume of space larger than the Sun and contains ionized particles ejected from sources including volcanoes on Io, one of Jupiter’s moons. A sulfur ion (S+) in Jupiter’s magnetic field has mass 5.32 x 10-26 kg and kine
> Figure CQ19.16 shows four permanent magnets, each having a hole through its center. Notice that the blue and yellow magnets are levitated above the red ones. (a) How does this levitation occur? (b) What purpose do the rods serve? (c) What can you say abo
> Consider the mass spectrometer shown schematically in Figure P19.15. The electric field between the plates of the velocity selector is 9.50 x 102 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.9
> How can a current loop be used to determine the presence of a magnetic field in a given region of space?
> A square and a circular loop with the same area lie in the xy - plane, where there is a uniform magnetic field B( pointing at some angle θ with respect to the positive z - direction. Each loop carries the same current, in the same direction. Which magnet
> An electron moves in a circular path perpendicular to a magnetic field of magnitude 0.235 T. If the kinetic energy of the electron is 3.30 x 10-19 J, find (a) The speed of the electron and (b) The radius of the circular path.
> Why do charged particles from outer space, called cosmic rays, strike Earth more frequently at the poles than at the equator?
> At the equator, near the surface of Earth, the magnetic field is approximately 50.0 μT northward, and the electric field is about 100. N/C downward in fair weather. Find the gravitational, electric, and magnetic forces on an electron with an instantaneou
> Is the magnetic field created by a current loop uniform? Explain.
> A proton moving at 4.00 x 106 m/s through a magnetic field of magnitude 1.70 T experiences a magnetic force of magnitude 8.20 x 10-13 N. What is the angle between the proton’s velocity and the field?
> A magnet attracts a piece of iron. The iron can then attract another piece of iron. On the basis of domain alignment, explain what happens in each piece of iron.
> Electrons and protons travel from the Sun to the Earth at a typical velocity of 4.00 x 105 m/s in the positive x - direction. Thousands of miles from Earth, they interact with Earth’s magnetic field of magnitude 3.00 x 10-8 T in the positive z - directio
> A laboratory electromagnet produces a magnetic field of magnitude 1.50 T. A proton moves through this field with a speed of 6.00 x 106 m/s. (a) Find the magnitude of the maximum magnetic force that could be exerted on the proton. (b) What is the magnitud
> Can a constant magnetic field set a proton at rest into motion? Explain your answer.
> As a charged particle moves freely in a circular path in the presence of a constant magnetic field applied perpendicular to the particle’s velocity, the particle’s kinetic energy (a) Remains constant, (b) Increases, or (c) Decreases.
> The circuit in Figure P18.62 contains two resistors, R1 = 2.0 kΩ and R2 = 3.0 kΩ, and two capacitors, C1 = 2.0 μF and C2 = 3.0 μF, connected to a battery with emf ε = 120 V. If there are no
> A battery with an internal resistance of 10.0 Ω produces an open circuit voltage of 12.0 V. A variable load resistance with a range from 0 to 30.0 Ω is connected across the battery. (Note: A battery has a resistance that depends o
> For the network in Figure P18.60, show that the resistance between points a and b is Rab = 27/17 Ω. (Hint: Connect a battery with emf ε across points a and b and determine ε/I, where I is the current in the battery.)
> A voltage DV is applied to a series configuration of n resistors, each of resistance R. The circuit components are reconnected in a parallel configuration, and voltage ΔV is again applied. Show that the power consumed by the series configuration is 1/n2
> A circuit consists of three identical lamps, each of resistance R, connected to a battery as in Figure P18.53. (a) Calculate an expression for the equivalent resistance of the circuit when the switch is open. Repeat the calculation when the switch is clo
> The circuit in Figure P18.52a consists of three resistors and one battery with no internal resistance. (a) Find the current in the 5.00 - Ω resistor. (b) Find the power delivered to the 5.00 - Ω resistor. (c) In each of the circui
> When two unknown resistors are connected in series with a battery, the battery delivers 225 W and carries a total current of 5.00 A. For the same total current, 50.0 W is delivered when the resistors are connected in parallel. Determine the value of each
> Three 60.0 - W, 120 - V light-bulbs are connected across a 120 - V power source, as shown in Figure P18.50. Find (a) The total power delivered to the three bulbs and (b) The potential difference across each. Assume the resistance of each bulb is constant
> Figure P18.49 shows separate series and parallel circuits. (a) What is the ratio ΔVseries /ΔVparallel? (b) What is the ratio of the power dissipated by the resistors in the series to the parallel circuit, Pseries/Pparallel? Figur
> The resistor R in Figure P18.58 dissipates 20 W of power. Determine the value of R. Figure P18.58:
> For the circuit shown in Figure P18.48, the voltmeter reads 6.0 V and the ammeter reads 3.0 mA. Find (a) The value of R, (b) The emf of the battery, and (c) The voltage across the 3.0 – kΩ resistor. (d) What assumptions did
> (a) Calculate the potential difference between points a and b in Figure P18.47 and (b) Identify which point is at the higher potential. Figure P18.47:
> How many different resistance values can be constructed from a 2.0 - Ω, a 4.0 - Ω, and a 6.0 - Ω resistor? Show how you would get each resistance value either individually or by combining them.
> Using Figure 18.29b and the results of Problems 18.43d and 18.44a, find the power supplied by the axon per action potential. Figure 18.29b:
> Consider the model of the axon as a capacitor from Problem 43 and Figure P18.43. (a) How much energy does it take to restore the inner wall of the axon to -7.0 x 10-2 V, starting from +3.0 x 10-2 V? (b) Find the average current in the axon wall during th
> Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration = 50.0 m/s x 2.0 x 10-3 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+
> A coffee maker is rated at 1200 W, a toaster at 1100 W, and a waffle maker at 1400 W. The three appliances are connected in parallel to a common 120 - V household circuit. (a) What is the current in each appliance when operating independently? (b) What t
> A heating element in a stove is designed to dissipate 3.00 x 103 W when connected to 240. V. (a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to 120. V. (b) Calculate the power it dissipates at that
> A 1 150 - W toaster and an 825 - W microwave oven are connected in parallel to the same 20.0 - A, 120 - V circuit. (a) Find the toaster’s resistance R. (b) If the microwave fails and is replaced, what maximum power rating can be used without tripping the
> What minimum number of 75 - W light-bulbs must be connected in parallel to a single 120 - V household circuit to trip a 30.0 - A circuit breaker?
> The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P18.57). The unknown resistance Rx is between points C and E. Point E is a “true ground”
> The capacitor in Figure P18.35 is uncharged for t (a) t = 0, when the switch is closed, and (b) t = (, one time constant after the switch is closed. Figure P18.35:
> Figure P18.37 shows a simplified model of a cardiac defibrillator, a device used to resuscitate patients in ventricular fibrillation. When the switch S is toggled to the left, the capacitor C charges through the resistor R. When the switch is toggled to
> The RC charging circuit in a camera flash unit has a voltage source of 275 V and a capacitance of 125 μF. (a) Find its resistance R if the capacitor charges to 90.0% of its final value in 15.0 s. (b) Find the average current delivered to the flash bulb i
> Consider a series RC circuit as in Figure P18.35 for which R = 1.00 MΩ, C = 5.00 μF, and ε = 30.0 V. Find (a) The time constant of the circuit and (b) The maximum charge on the capacitor after the switch is thrown c
> An uncharged capacitor and a resistor are connected in series to a source of emf. If ε = 9.00 V, C = 20.0 μF, and R = 1.00 x 102 Ω, find (a) The time constant of the circuit, (b) The maximum charge on the capacitor, and (c) The charge on the capacitor af
> Consider the series RC circuit shown in Figure 18.17 for which R = 75.0 kΩ, C = 25.0 μF, and ε = 12.0 V. Find (a) The time constant of the circuit and (b) The charge on the capacitor one time constant after the swit
> Show that ( = RC has units of time.
> Find the potential difference across each resistor in Figure P18.31. Figure P18.31:
> For the circuit shown in Figure P18.30, use Kirchhoff’s rules to obtain equations for (a) The upper loop, (b) The lower loop, and (c) The node on the left side. In each case suppress units for clarity and simplify, combining like terms.
> (a) Can the circuit shown in Figure P18.29 be reduced to a single resistor connected to the batteries? Explain. (b) Find the magnitude of the current and its direction in each resistor. Figure P18.29:
> An emf of 10 V is connected to a series RC circuit consisting of a resistor of 2.0 x 106 Ω and an initially uncharged capacitor of 3.0 μF. Find the time required for the charge on the capacitor to reach 90% of its final value.
> A dead battery is charged by connecting it to the live battery of another car with jumper cables (Fig. P18.28). Determine the current in (a) The starter and in (b) The dead battery. Figure P18.28:
> (a) Can the circuit shown in Figure P18.27 be reduced to a single resistor connected to the batteries? Explain. (b) Calculate each of the unknown currents I1, I2, and I3 for the circuit. Figure P18.27:
> Figure P18.26 shows a voltage divider, a circuit used to obtain a desired voltage ΔVout from a source voltage ε. Determine the required value of R2 if ε = 5.00 V, ΔVout = 1.50 V, and R1 = 1.00 x 103 &Icir
> Using Kirchhoff’s rules, (a) Find the current in each resistor shown in Figure P18.25 and (b) Find the potential difference between points c and f. Figure P18.25:
> Four resistors are connected to a battery with a terminal voltage of 12 V, as shown in Figure P18.24. (a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of
> In the circuit of Figure P18.23, determine (a) The current in each resistor, (b) The potential difference across the 2.00 x 102 - Ω resistor, and (c) The power delivered by each battery. Figure P18.23:
> In the circuit of Figure P18.22, the current I1 is 3.0 A and the values of ε and R are unknown. What are the currents I2 and I3? Figure P18.22:
> Taking R = 1.00 kΩ and ε = 250. V in Figure P18.21, determine the direction and magnitude of the current in the horizontal wire between a and e. Figure P18.21:
> For the circuit shown in Figure P18.20, calculate (a) The current in the 2.00 - Ω resistor and (b) The potential difference between points a and b, ΔV = Vb – V. Figure P18.20:
> Figure P18.19 shows a Wheatstone bridge, a circuit used to precisely measure an unknown resistance R by varying Rvar until the ammeter reads zero current and the bridge is said to be “balanced.” If the bridge is balanc
> The circuit in Figure P18.55 has been connected for several seconds. Find the current (a) In the 4.00 - V battery, (b) In the 3.00 - Ω resistor, (c) In the 8.00 - V battery, and (d) In the 3.00 - V battery. (e) Find the charge on the capacito
> (a) Find the current in each resistor of Figure P18.18 by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoff’s laws: one with the node rule; a second using
> (a) You need a 45 - Ω resistor, but the stockroom has only 20. - Ω and 50. - Ω resistors. How can the desired resistance be achieved under these circumstances? (b) What can you do if you need a 35 - Ω resistor?
> (a) Is it possible to reduce the circuit shown in Figure P18.16 to a single equivalent resistor connected across the battery? Explain. (b) Find the current in the 2.00 - Ω resistor. (c) Calculate the power delivered by the battery to the circ
> Find the current in the 12 - Ω resistor in Figure P18.15. Figure P18.15:
> A 2.00 - nF capacitor with an initial charge of 5.10 μC is discharged through a 1.30 – kΩ resistor. (a) Calculate the magnitude of the current in the resistor 9.00 μs after the resistor is connected across the terminals of the capacitor. (b) What charge
