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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

The plane of a square loop of wire with edge length a = 0.200 m is perpendicular to the Earth€™s magnetic field at a point where B = 15.0 /T, as shown in Figure P31.55. The total resistance
Magnetic field values are often determined by using a device known as a search coil. This technique depends on the measurement of the total charge passing through a coil in a time interval during
In Figure P31.57, the rolling axle, 1.50m long, is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 Ω is connected to the rails at points a and b, directly
A conducting rod moves with a constant velocity v in a direction perpendicular to a long, straight wire carrying a current I as shown in Figure P31.58. Show that the magnitude of the emf generated
A circular loop of wire of radius r is in a uniform magnetic field, with the plane of the loop perpendicular to the direction of the field (Fig. P31.59). The magnetic field varies with time according
In Figure P31.60, a uniform magnetic field decreases at a constant rate dB/dt =- K, where K is a positive constant. A circular loop of wire of radius a containing a resistance R and a capacitance C
A rectangular coil of 60 turns, dimensions 0.100 m by 0.200 m and total resistance 10.0 (, rotates with angular speed 30.0 rad/s about the y axis in a region where a 1.00-T magnetic field is directed
A small circular washer of radius 0.500 cm is held directly below a long, straight wire carrying a current of 10.0 A The washer is located 0.500 m above the top of a table (Fig. P31.62)(a) If the
A conducting rod of length ℓ moves with velocity v parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance
A rectangular loop of dimensions ℓ and w moves with a constant velocity v away from a long wire that carries a current I in the plane of the loop (Fig. P31.64). The total resistance of the loop
The magnetic flux through a metal ring varies with time t according to ΦB = 3(at3 - bt2) T|∙|m2, with a = 2.00 s-3 and b = 6.00 s-2. The resistance of the ring is 3.00 Ω. Determine
The bar of mass m in Figure P31.66 is pulled horizontally across parallel rails by a mass less string that passes over an ideal pulley and is attached to a suspended object of mass M. The uniform
A solenoid wound with 2 000 turns/m is supplied with current that varies in time according to I = (4A) sin (120πt), where t is in seconds. A small coaxial circular coil of 40 turns and radius r
Figure P31.68 shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 50.0 cm. It is placed in a constant magnetic field of 0.500 T directed out
A betatron accelerates electrons to energies in the MeV range by means of electromagnetic induction. Electrons in a vacuum chamber are held in a circular orbit by a magnetic field perpendicular to
A wire 30.0 cm long is held parallel to and 80.0 cm above a long wire carrying 200 A and resting on the floor (Fig. P31.70). The 30.0-cm wire is released and falls, remaining parallel with the
A long, straight wire carries a current that is given by I = Imax sin (wt + 2ǿ) and lies in the plane of a rectangular coil of N turns of wire, as shown in Figure P31.9. The quantities Imax, w,
A dime is suspended from a thread and hung between the poles of a strong horseshoe magnet as shown in Figure P31.72. The dime rotates at constant angular speed w about a vertical axis. Letting
Determine the initial direction of the deflection of charged particles as they enter the magnetic fields as shown in Figure P29.1.
Consider an electron near the Earth’s equator. In which direction does it tend to deflect if its velocity is directed? (a) Downward, (b) Northward, (c) Westward, or (d) Southeastward?
An electron moving along the positive x axis perpendicular to a magnetic field experiences a magnetic deflection in the negative y direction. What is the direction of the magnetic field?
A proton travels with a speed of 3.00 % 106 m/s at an angle of 37.0° with the direction of a magnetic field of 0.300 T in the 'y direction. What are? (a) The magnitude of the magnetic force on the
A proton moves perpendicular to a uniform magnetic field B at 1.00 % 107 m/s and experiences an acceleration of 2.00 x 1013 m/s2 in the 'x direction when its velocity is in the + z direction.
An electron is accelerated through 2 400 V from rest and then enters a uniform 1.70-T magnetic field. What are? (a) The maximum and (b) The minimum values of the magnetic force this charge can
A proton moving at 4.00 % 106 m/s through a magnetic field of 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?
At the equator, near the surface of the Earth, the magnetic field is approximately 50.0 +T northward, and the electric field is about 100 N/C downward in fair weather. Find the gravitational,
A proton moves with a velocity of v = (2i - 4j +k) m/s in a region in which the magnetic field is B = (i = 2j - 3k) T. What is the magnitude of the magnetic force this charge experiences?
An electron has a velocity of 1.20 x 104 m/s (in the positive x direction), and an acceleration of 2.00 x 1012 m/s2 (in the positive z direction) in a uniform electric and magnetic field. If the
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
A wire carries a steady current of 2.40 A. A straight section of the wire is 0.750 m long and lies along the x axis within a uniform magnetic field, B = 1.60kˆ T. If the current is in the + x
A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire assuming the angle
A conductor suspended by two flexible wires as shown in Figure P29.14 has a mass per unit length of 0.040 0 kg/m. What current must exist in the conductor in order for the tension in the supporting
A rod of mass 0.720 kg and radius 6.00 cm rests on two parallel rails (Fig. P29.15) that are d = 12.0 cm apart and L = 45.0 cm long. The rod carries a current of I = 48.0 A (in the direction shown)
A rod of mass m and radius R rests on two parallel rails (Fig. P29.15) that are a distance d apart and have a length L, the rod carries a current I (in the direction shown) and rolls along the rails
A non-uniform magnetic field exerts a net force on a magnetic dipole. A strong magnet is placed under a horizontal conducting ring of radius r that carries current I as shown in Figure P29.17. If the
In Figure P29.18, 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
Assume that in Atlanta, Georgia, the Earth’s magnetic field is 52.0 +T northward at 60.0° below the horizontal. A tube in a neon sign carries current 35.0 mA, between two diagonally opposite
A current of 17.0 mA is maintained in a single circular loop of 2.00 m circumference. A magnetic field of 0.800 T is directed parallel to the plane of the loop. (a) Calculate the magnetic moment of
A small bar magnet is suspended in a uniform 0.250-T magnetic field. The maximum torque experienced by the bar magnet is 4.60 x 10-3 N∙m. Calculate the magnetic moment of the bar magnet.
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,
A rectangular coil consists of N = 100 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle θ = 30.0° with
A 40.0-cm length of wire carries a current of 20.0 A. It is bent into a loop and placed with its normal perpendicular to a magnetic field with a magnitude of 0.520 T. What is the torque on the loop
A current loop with magnetic dipole moment μ is placed in a uniform magnetic field B, with its moment making angle θ with the field. With the arbitrary choice of U = 0 for θ = 90°,
The needle of a magnetic compass has magnetic moment 9.70 mA#m2. At its location, the Earth’s magnetic field is 55.0 +T north at 48.0° below the horizontal. (a) Identify the orientations of the
A wire is formed into a circle having a diameter of 10.0 cm and placed in a uniform magnetic field of 3.00 mT. The wire carries a current of 5.00 A. Find (a) The maximum torque on the wire and
The rotor in a certain electric motor is a flat rectangular coil with 80 turns of wire and dimensions 2.50 cm by 4.00 cm. The rotor rotates in a uniform magnetic field of 0.800 T. When the plane of
The magnetic field of the Earth at a certain location is directed vertically downward and has a magnitude of 50.0 +T. A proton is moving horizontally toward the west in this field with a speed of
A singly charged positive ion has a mass of 3.20 x 10-26 kg. After being accelerated from rest through a potential difference of 833 V, the ion enters a magnetic field of 0.920 T along a direction
One electron collides elastically with a second electron initially at rest. After the collision, the radii of their trajectories are 1.00 cm and 2.40 cm. The trajectories are perpendicular to a
A proton moving in a circular path perpendicular to a constant magnetic field takes 1.00 μs to complete one revolution. Determine the magnitude of the magnetic field.
A proton (charge + e, mass mp), a deuteron (charge + e, mass 2mp), and an alpha particle (charge + 2e, mass 4mp) are accelerated through a common potential difference 0V. Each of the particles enters
An electron moves in a circular path perpendicular to a constant magnetic field of magnitude 1.00 mT. The angular momentum of the electron about the center of the circle is 4.00 x 10-25 J s.
Calculate the cyclotron frequency of a proton in a magnetic field of magnitude 5.20 T.
A singly charged ion of mass m is accelerated from rest by a potential difference ∆V. It is then deflected by a uniform magnetic field (perpendicular to the ion’s velocity) into a semicircle
A cosmic-ray proton in interstellar space has energy of 10.0 MeV and executes a circular orbit having a radius equal to that of Mercury’s orbit around the Sun (5.80 x 1010 m). What is the magnetic
Figure 29.21 shows a charged particle traveling in a non-uniform magnetic field forming a magnetic bottle. (a) Explain why the positively charged particle in the figure must be moving clockwise.
A singly charged positive ion moving at 4.60 x 105 m/s leaves a circular track of radius 7.94 mm along a direction perpendicular to the 1.80-T magnetic field of a bubble chamber. Compute the mass (in
A velocity selector consists of electric and magnetic fields described by the expressions E = Ek and B = Bj, with B = 15.0 mT. Find the value of E such that a 750-eV electron moving along the
Singly charged uranium-238 ions are accelerated through a potential difference of 2.00 kV and enter a uniform magnetic field of 1.20 T directed perpendicular to their velocities. (a) Determine the
Consider the mass spectrometer shown schematically in Figure 29.24. The magnitude of the electric field between the plates of the velocity selector is 2 500 V/m, and the magnetic field in both the
A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.450 T over a region of radius 1.20 m. What are? (a) The cyclotron frequency and (b) The maximum speed acquired by
What is the required radius of a cyclotron designed to accelerate protons to energies of 34.0 MeV using a magnetic field of 5.20 T?
A cyclotron designed to accelerate protons has an outer radius of 0.350 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 600 V each time they cross
At the Fermilab accelerator in Batavia, Illinois, protons having momentum 4.80 x 10-16 kg #m/s are held in a circular orbit of radius 1.00 km by an upward magnetic field. What is the magnitude of
The picture tube in a television uses magnetic deflection coils rather than electric deflection plates. Suppose an electron beam is accelerated through a 50.0-kV potential difference and then through
A flat ribbon of silver having a thickness t = 0.200 mm is used in a Hall-effect measurement of a uniform magnetic field perpendicular to the ribbon, as shown in Figure P29.48. The Hall coefficient
A flat copper ribbon 0.330 mm thick carries a steady current of 50.0 A and is located in a uniform 1.30-T magnetic field directed perpendicular to the plane of the ribbon. If a Hall voltage of 9.60
A Hall-effect probe operates with a 120-mA current. When the probe is placed in a uniform magnetic field of magnitude 0.080 0 T, it produces a Hall voltage of 0.700 +V. (a) When it is measuring an
In an experiment that is designed to measure the Earth’s magnetic field using the Hall effect a copper bar 0.500 cm thick is positioned along an east–west direction. If a current of 8.00 A in the
Assume that the region to the right of a certain vertical plane contains a vertical magnetic field of magnitude 1.00 mT, and the field is zero in the region to the left of the plane. An electron,
Sodium melts at 99°C. Liquid sodium, an excellent thermal conductor, is used in some nuclear reactors to cool the reactor core. The liquid sodium is moved through pipes by pumps that exploit the
A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient
Protons having a kinetic energy of 5.00 MeV are moving in the positive x direction and enter a magnetic field B = 0.050 0kË† T directed out of the plane of the page and extending from x = 0
(a) A proton moving in the + x direction with velocity v = vii experiences a magnetic force F = Fij in the +y direction. Explain what you can and cannot infer about B from this information. (b)
A positive charge q = 3.20 x 10-19 C moves with a velocity v = (2i + 3j - k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total
A wire having a linear mass density of 1.00 g/cm is placed on a horizontal surface that has a coefficient of kinetic friction of 0.200. The wire carries a current of 1.50 A toward the east and slides
Electrons in a beam are accelerated from rest through a potential difference 0V. The beam enters an experimental chamber through a small hole. As shown in Figure P29.59, the electron velocity vectors
A proton is at rest at the plane vertical boundary of a region containing a uniform vertical magnetic field B. An alpha particle moving horizontally makes a head-on elastic collision with the proton.
The circuit in Figure P29.61 consists of wires at the top and bottom and identical metal springs in the left and right sides. The upper portion of the circuit is fixed. The wire at the bottom has a
A hand-held electric mixer contains an electric motor. Model the motor as a single flat compact circular coil carrying electric current in a region where a magnetic field is produced by an external
A non-conducting sphere has mass 80.0 g and radius 20.0 cm. A flat compact coil of wire with 5 turns is wrapped tightly around it, with each turn concentric with the sphere. As shown in Figure
A metal rod having a mass per unit length A carries a current I. The rod hangs from two vertical wires in a uniform vertical magnetic field as shown in Figure P29.64. The wires make an angle θ
A cyclotron is sometimes used for carbon dating, as described in Chapter 44. Carbon-14 and carbon-12 ions are obtained from a sample of the material to be dated, and accelerated in the cyclotron. If
A uniform magnetic field of magnitude 0.150 T is directed along the positive x axis. A positron moving at 5.00 x 106 m/s enters the field along a direction that makes an angle of 85.0° with the x
Consider an electron orbiting a proton and maintained in a fixed circular path of radius R = 5.29 x 10-11 m by the Coulomb force. Treating the orbiting charge as a current loop, calculate the
A singly charged ion completes five revolutions in a uniform magnetic field of magnitude 5.00 x 10-2 T in 1.50 ms. Calculate the mass of the ion in kilograms.
A proton moving in the plane of the page has a kinetic energy of 6.00 MeV. A magnetic field of magnitude B = 1.00 T is directed into the page. The proton enters the magnetic field with its velocity
Table P29.70 shows measurements of a Hall voltage and corresponding magnetic field for a probe used to measure magnetic fields.(a) Plot these data, and deduce a relationship between the two
A heart surgeon monitors the flow rate of blood through an artery using an electromagnetic flow meter (Fig. P29.71). Electrodes A and B make contact with the outer surface of the blood vessel, which
As shown in Figure P29.72, a particle of mass m having positive charge q is initially traveling with velocity vj . At the origin of coordinates it enters a region between y = 0 and y = h containing a
In Niels Bohr’s 1913 model of the hydrogen atom, an electron circles the proton at a distance of 5.29 x 10-11 m with a speed of 2.19 x 106 m/s. Compute the magnitude of the magnetic field that this
A lightning bolt may carry a current of 1.00 x 104 A for a short period of time. What is the resulting magnetic field 100 m from the bolt? Suppose that the bolt extends far above and below the point
(a) A conductor in the shape of a square loop of edge length ℓ = 0.400 m carries a current I = 10.0 A as in Fig. P30.3. Calculate the magnitude and direction of the magnetic field at the center
Calculate the magnitude of the magnetic field at a point 100 cm from a long, thin conductor carrying a current of 1.00 A.
Determine the magnetic field at a point P located a distance x from the corner of an infinitely long wire bent at a right angle, as shown in Figure P30.5. The wire carries a steady current I.
A conductor consists of a circular loop of radius R and two straight, long sections, as shown in Figure P30.6. The wire lies in the plane of the paper and carries a current I. Find an expression for
The segment of wire in Figure P30.7 carries a current of I = 5.00 A, where the radius of the circular arc is R = 3.00 cm. Determine the magnitude and direction of the magnetic field at the origin.
Consider a flat circular current loop of radius R carrying current I. Choose the x axis to be along the axis of the loop, with the origin at the center of the loop. Plot a graph of the ratio of the
Two very long, straight, parallel wires carry currents that are directed perpendicular to the page, as in Figure P30.9. Wire 1 carries a current I1 into the page (in the €“z direction) and
A very long straight wire carries current I. In the middle of the wire a right-angle bend is made. The bend forms an arc of a circle of radius r, as shown in Figure P30.10. Determine the magnetic

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