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physics
particle physics

Questions and Answers of Particle Physics

For a given current loop, a rectangular geometry can make calculations more convenient than a circular geometry. How would the magnetic field from a small square current loop compare with that from a
A circular current-carrying wire loop produces a magnetic field. A spinning disk of uniformly distributed charge produces a similar magnetic field. How would you expect the field due to a spinning
For the bar magnet in Figure P28.18, which of the four locations labeled 1,2,3,4 has the greatest density of magnetic field lines?Data from Figure P28.18 N d 2 P.P. d S 3
A negatively charged particle located at the origin of an \(x y z\) coordinate system is spinning clockwise about the \(x\) axis (that is, clockwise when you look at the particle while standing
Figure P28.20 shows a wire segment bent into a halfcircle, with the center of curvature labeled \(P\). If the wire of which this segment is a part is extremely long and carries a current \(I\), what
In the Bohr model of the hydrogen atom, an electron orbits a nucleus consisting of one proton. Given that the electron and proton are both spinning, describe the types of magnetic interactions you
In the space surrounding Earth, the main component of the planet's magnetic field is the field due to a magnetic dipole. In what direction is Earth's magnetic dipole moment?
Earth's magnetic field is thought to be generated by currents in the planet's core. In what direction (clockwise or counterclockwise, when viewed along the rotation axis from north to south) does
The disk shown in Figure P28.24 is charged with electrons and spins counterclockwise when viewed from above. From this perspective, what is the direction of the magnetic dipole moment of the
In the open wire loop of Figure P28.25, end 1 is held at a higher electric potential than end 2. (a) In which direction do electrons move through the loop? (b) What is the direction of the current?
Figure P28.26 shows part of the rotation of an electric motor, during which the magnetic dipole moment of the loop points to the left or has some component to the left. If the entire rotation were
A current loop lying in the \(x y\) plane of an \(x y z\) coordinate system experiences a torque that is clockwise about the \(y\) axis when viewed looking down from the positive \(y\) axis toward
A current loop lies in the \(x y\) plane of an \(x y z\) coordinate system, with the current circulating counterclockwise when viewed looking down the positive \(z\) axis toward the origin. The loop
Determine the direction of the magnetic dipole moment in each current loop or charge distribution in Figure P28.29. In (c), the higher potential end of the loop is marked + , and in (d), the disk has
(a) As the electric motor shown schematically in Figure P28.30 operates, which of the arrows shown could represent the magnetic dipole moment at various instants? (b) If there are any arrows that are
Figure P28.31 shows a rectangular loop of current in an external magnetic field. Initially the plane of the loop makes a \(65^{\circ}\) angle with the magnetic field. (a) Determine the direction of
Figure 28. 10 shows a current loop in an external magnetic field and the forces exerted on the different lengths of the wire. Assume that the loop is attached to a pivot that allows it to spin (as
A negatively charged particle is held in position and then released in a region where a uniform magnetic field points in the positive \(x\) direction and a uniform electric field points in the
The current loop in Figure P28.34 lies in the \(x y\) plane. For each of the Amperrian paths (a)-(e), is the line integral of the magnetic field positive, negative, or zero?Data from Figure P28.34
Wires 1 to 5 in Figure P28.35 carry current either into or out of the page. What is the magnitude of the current enclosed by the Ampèrian path indicated? Is the line integral of the magnetic field
Is the line integral of the magnetic field along the closed path in Figure P28.36 positive, negative, or zero? The direction of integration is shown with arrows on the path.Data from Figure P28.36
Figure P28.37 shows a series of current-carrying wires, and in each case an Ampèrian path is shown (but without direction). Rank the six cases according to the magnitude of the line integral of the
The line integral of the magnetic field around a certain closed path is initially \(L\). The current that penetrates this path is then doubled. What can you say about the current through the path if
Each of the wires 1 to 3 in Figure P28.39 carries a current perpendicular to the page. The line integrals of the magnetic field around the three Ampèrian paths shown all have the same positive
A positively charged particle located at the origin of an \(x y z\) coordinate system spins about the \(z\) axis, and the spin is counterclockwise when viewed looking down from the positive \(z\)
Eleven wires and one Ampèrian path are shown in Figure P28.41, with current values and directions as indicated. Is the line integral of the magnetic field along the Ampèrian path shown greater
Figure P28.42 shows magnetic field lines in a certain region. Are there any locations where there must be a current directed into or out of the plane of the diagram? (Consider locations near the
Figure \(\mathrm{P} 28. 43\) shows two paths (A and B) around a wire that carries current \(I\). (a) Along which path is the line integral of the magnetic field greater? (b) Along which path is the
Figure P28.44 shows a very long wire that carries a current \(I\) in the \(z\) direction and is centered in the \(x y\) plane at the position \((0,0)\). The line integral of the magnetic field along
At a location \(25 \mathrm{~mm}\) away from a long, straight currentcarrying wire, the magnitude of the magnetic field due to the wire is \(2.0 \times 10^{-5} \mathrm{~T}\). Calculate the magnitude
A long, straight wire carrying \(1.5 \mathrm{~A}\) of current to the left is placed above a large, flat sheet through which the current per unit width is \(3.0 \mathrm{~A} / \mathrm{m}\) to the left.
The magnetic field magnitude is \(4.0 \mathrm{mT}\) at a position \(6.2 \mathrm{~mm}\) radially away from a long current-carrying wire. Calculate \((a)\) the current in the wire and \((b)\) the
Two straight wires separated by a very small distance run parallel to each other, one carrying a current of \(3.0 \mathrm{~A}\) to the right and the other carrying a current of 4. 0 A to the left.
A moving particle carrying charge \(e\) traveling to the right at \(2.5 \times 10^{7} \mathrm{~m} / \mathrm{s}\) initially feels no magnetic force. When a long current-carrying wire is placed
An electric current is uniformly distributed throughout a long, straight wire that has a diameter of \(50 \mathrm{~mm}\). If the current through the wire is \(6.0 \mathrm{~A}\), calculate the
Two large, flat current-carrying sheets are placed parallel to each other, one sheet above the other. The upper sheet carries a current density of \(2.0 \mathrm{~A} / \mathrm{m}\) to the left, and
An electron travels to the right at \(3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\) between two large, flat sheets that are parallel to each other and to the electron's line of motion. If currents per
A certain wire has a circular cross section of radius \(R\) and carries a current \(I\). Suppose that the charge carriers all move along the cylindrical surface of the wire, not through its
Point \(\mathrm{P}\) is a distance \(d_{1}=4.0 \mathrm{~mm}\) above a large sheet of metal that carries a current of \(40 \mathrm{~A}\) in the positive \(x\) direction and a distance \(d_{2}=3.0
Two large, parallel, current-carrying plates are oriented horizontally and the vertical distance between them is \(5.0 \mathrm{~mm}\). The current per unit width in each plate is \(100 \mathrm{~A} /
A particle of mass \(9.1 \times 10^{-31} \mathrm{~kg}\) and carrying an unknown quantity of charge is shot at a velocity of \(2.0 \times 10^{4} \mathrm{~m} / \mathrm{s}\) to the right and enters the
A long solenoid with 300 windings per meter of length carries a current of \(1.0 \mathrm{~A}\). Calculate the magnitude of the magnetic field inside the solenoid.
You need to use a long solenoid to produce a magnetic field of magnitude \(0.070 \mathrm{~T}\). If the maximum current you are able to run through the windings is \(20 \mathrm{~A}\), what is the
A small solenoid is inserted into a larger solenoid (Figure P28.60). The current in the small solenoid is from A to B. (a) Determine the initial direction of the magnetic dipole moment of the small
A long, straight wire carrying a current of \(2.5 \mathrm{~A}\) to the left is placed directly below and parallel to the central axis of a solenoid that has 1000 windings per meter of length and a
Calculate the magnitude of the magnetic force exerted on a wire that is \(20 \mathrm{~mm}\) long and carries a current of \(4.0 \mathrm{~A}\) when it is suspended inside a solenoid at an angle of
A toroid has 250 square windings carrying a current of \(3.0 \mathrm{~mA}\). Each side of each square winding is \(50 \mathrm{~mm}\) long, and the distance from the toroid center to the inner surface
At what radial distance \(r\) from the center of a toroid of 200 windings does the magnitude of the magnetic field equal that found inside a solenoid that has 500 turns per meter of length? Assume
A toroid carries a current \(I\) and has \(n\) circular windings per unit length measured along the inside edge of the windings. The radius of each circular winding is \(R_{\text {winding }}\), and
An electron is fired into one end of the solenoid in Figure P28.66. Viewed along the positive \(x\) axis from a negative \(x\) coordinate, the electron enters from below at a \(65^{\circ}\) angle to
You are calibrating magnetic coils for a particle detector. One step involves checking the magnetic field at different positions inside a toroid, and you are asked to measure the field at the
Calculate the magnitude of the magnetic field at the center of a circular arc of radius \(25 \mathrm{~mm}\) spanning an angle of \(\pi / 2\) and carrying a current of \(3.0 \mathrm{~A}\).
Wire \(1,5.0 \mathrm{~m}\) long and carrying a current of \(3.0 \mathrm{~A}\), experiences a magnetic force of magnitude \(4.0 \times 10^{-7} \mathrm{~N}\) when placed \(90 \mathrm{~mm}\) away from
Use the Biot-Savart law to determine the magnetic field \(70 \mathrm{~mm}\) above the center of a loop of wire that has a radius of \(0.22 \mathrm{~m}\) and carries \(3.0 \mathrm{~A}\) of current.
Wire \(1,3.0 \mathrm{~m}\) long and of linear mass density \(0.010 \mathrm{~kg} / \mathrm{m}\), is initially held in place and carries \(10 \mathrm{~A}\) of current to the right. Very long wire 2 is
Suppose that we can use wire of \(1.0-\mathrm{mm}\) diameter to make either a single loop of wire or a solenoid, and we wish to compare, for a given current, the magnetic fields at the center of
In Figure P28.73, point P is the common center of two circular arcs of wire, the larger of radius \(70 \mathrm{~mm}\) and the smaller of radius \(20 \mathrm{~mm}\). What are the magnitude and
A current-carrying wire has been bent into the form shown in Figure P28.74, with a half-circle of radius \(R_{1}\) lying in the \(x y\) plane connected via two straight segments to a half-circle of
A wire carrying a \(3.0-\mathrm{A}\) current lies along the \(x\) axis of an \(x y\) coordinate system, extending from \(x=0\) to \(x=10 \mathrm{~m}\). What is the magnitude of the magnetic field at
The horizontal portion of the wire in Figure P28.76 has a length \(\ell=0.100 \mathrm{~m}\), and position \(\mathrm{P}\) is a perpendicular distance \(d=30.0 \mathrm{~mm}\) above the center of the
An electron moves in a straight line at a speed of \(6.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\). Calculate the magnitude and direction of the magnetic field at a position \(5.0 \mathrm{~mm}\)
A proton moves in the positive \(x\) direction at \(4.00 \times 10^{4} \mathrm{~m} / \mathrm{s}\). Calculate the magnitude of the magnetic field at the point \((x, y)=(+2.00 \mathrm{~mm},+1.00
Express the magnetic field due to a uniformly moving charged particle in terms of the electric field of the particle and its velocity.
Two electrons 1 and 2 move along antiparallel paths separated by a distance of \(10 \mathrm{~nm}\), traveling at speeds \(v_{1}=\) \(4.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\) and \(v_{2}=7.0
Proton 1 , traveling in the negative \(x\) direction at speed \(v_{1}\), is directly below proton 2 , which is traveling at speed \(v_{2}\) at an angle of \(45^{\circ}\) above the positive \(x\)
A charged particle is traveling through a uniform magnetic field, with its velocity perpendicular to the field direction. You learned that such a particle experiences a magnetic force that causes it
Electron 1 , initially traveling to the right at \(1.5 \times 10^{6} \mathrm{~m} / \mathrm{s}\), is accelerated upward at \(900 \mathrm{~m} / \mathrm{s}^{2}\) by the electromagnetic force exerted by
An electron and a proton are fired in opposite directions, and at the instant they are nearest each other, their separation distance is \(3.0 \mu \mathrm{m}\) (Figure P28.84). At that instant, the
Two electrons move near each other and at the instant shown in Figure P28.85 are \(2.0 \mathrm{~mm}\) apart. The speed of electron 1 is \(v_{1}=300 \mathrm{~m} / \mathrm{s}\), that of electron 2 is
At \(t=0\), electron 1 is shot out of an accelerator at a speed of \(2.0 \times 10^{3} \mathrm{~m} / \mathrm{s}\). At \(t=1.0 \mu \mathrm{s}\), electron 2 is shot out of the accelerator and travels
A current loop lies in the \(x y\) plane, with the current circulating counterclockwise when viewed from the positive \(z\) axis. Is there a torque on the loop, and if so, in what direction, if a
A solenoid that is \(200 \mathrm{~mm}\) long has 200 turns. What current \(I\) in the solenoid is required to produce a magnetic field of magnitude \(1.0 \mathrm{~T}\) inside the solenoid?
Wire 1 is \(2.3 \mathrm{~m}\) long and carries a current of \(2.2 \mathrm{~A}\) to the right. Wire 2 is also \(2.3 \mathrm{~m}\) long, and it carries a current of 3. 0 A to the left. The wires are
Figure P28.90 shows two square loops of wire. The loop on the right is fixed in place, and the one on the left is free to pivot in any direction. Both loops carry a current that is counterclockwise
Wire 1, with mass \(0.010 \mathrm{~kg}\) and length \(1.0 \mathrm{~m}\), has a square cross section and is initially at rest on a table. It is connected by flexible leads to a battery and carries a
Two of your friends separately calculated a magnetic field line integral around a long, straight current-carrying wire in a homework problem, but they arrived at different answers. Now they want your
Your design team is working on an air-core toroid that is to have the greatest feasible magnetic field per ampere of current but in which the greatest magnetic field magnitude must be exactly four
Determine the direction of the magnetic force exerted at the center of the wire or on the particles in Figure 28. 20.Data from Figure 28. 20 Figure 28.20 (a) (b) N S S N +8 te
Determine the direction of the magnetic field at \(\mathrm{P}\) due to \((a)\) the current loop in Figure 28. 21a and (b) segments A and C of the current loop in Figure 28. 21b.Data from Figure 28.
Determine in which direction the current loop rotates \((a)\) in Figure \(28.21 c\) and \((b)\) in Figure 28. 21d.Data from Figure 28. 21 (a) ! 21 (e) (d) (2)
(a) Determine the currents encircled by the five Ampèrian paths in Figure 28. 21e. (b) Rank the paths according to the magnitudes of the line integral of the magnetic field along each path, greatest
When placed between the poles of a horseshoe magnet as shown in Figure 28.12, does a rectangular current loop experience a torque? If so, in which direction does the loop rotate?Data from Figure
Consider the Ampèrian path going through the collection of current-carrying wires in Figure 28.19. If the magnitude of the current is the same in all the wires, is the line integral of the magnetic
A long straight wire carries a current of magnitude \(I\), and this current creates a magnetic field \(\vec{B}\). Derive an expression for the magnitude of the magnetic field a radial distance \(r\)
A large flat metal sheet carries a current. The magnitude of the current per unit of sheet width is \(K\). What is the magnitude of the magnetic field a distance \(d\) above the sheet?
The toroid in Figure 28.31 has 1000 windings carrying a current of \(1.5 \mathrm{~mA}\). Each winding is a square of side length \(10 \mathrm{~mm}\), and the toroid's inner radius is \(10
A long straight wire carries a current of magnitude \(I\). Use the Biot-Savart law to derive an expression for the mag. netic field \(\vec{B}\) produced at point \(\mathrm{P}\) a radial distance
A wire bent into a circular arc of radius \(R\) subtending an angle \(\phi\) carries a current of magnitude \(I\) (Figure 28.35). Use the Biot-Savart law to derive an expression for the magnitude of
An electron carrying a charge \(-e=-1.60 \times 10^{-19} \mathrm{C}\) moves in a straight line at a speed \(v=3.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\). What are the magnitude and direction of the
What happens if the conducting rod in Figure P29.1 moves \((a)\) in either direction along the \(z\) axis and \((b)\) in either direction along the \(y\) axis?Data from Figure P29.1 B
The Air Force Thunderbirds aerial demonstration team is performing at an air show located on Earth's magnetic equator. In what directions can the airplanes fly so that there is no charge separation
How should any one of the airplanes described in Problem 2 fly in order to produce the maximum charge separation between its wing tips? (Consider both the direction of motion and the orientation of
Figure P29.4 shows a square conducting loop centered on the \(x\) axis, with its sides parallel to the \(y\) and \(z\) axes. The loop moves with constant velocity in the negative \(x\) direction
What happens if the conducting rod in Figure P29.1 rotates(a) clockwise about the \(z\) axis as viewed looking down the positive \(z\) axis toward the origin, \((b)\) clockwise about the \(x\) axis
The large loop of wire in Figure P29.6a carries into and out of a lamp an electric current whose direction alternates back and forth with time. A circular ring of wire of radius \(R\) is at one of
The bar magnet in Figure P29.7 is rotated about an axis that runs perpendicular to the page and passes through the center of the magnet. The magnet rotates with rotational speed \(\omega\). A loop of
A large region of space contains a uniform magnetic field that is increasing with time. You have a piece of wire of length \(\ell\) and want to form a coil from it. What shape should you use for your
A \(1.00-\mathrm{m}\) length of wire is shaped into a rectangle, and another \(1.00-\mathrm{m}\) length of identical wire is shaped into a circle. Both wires then move at the same speed into and then
You observe a small charge separation between the ends of a conducting rod that is lying on the table in front of you. This is puzzling because the rod is not connected to a battery or other power
A flat conducting plate is centered in the \(x y\) plane of an \(x y z\) coordinate system in which the \(x y\) plane is horizontal. A bar magnet is lowered vertically toward the plate. If the magnet

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