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physics
particle physics

Questions and Answers of Particle Physics

A proton is located in the \(x y\) plane at \((4.00 \mathrm{~mm}, 3. 00\) \(\mathrm{mm}\) ) and experiences an electric force exerted by a particle at the origin carrying a positive charge of \(6.95
A particle at the origin of a Cartesian coordinate system carries a charge of \(3.89 \times 10^{-9} \mathrm{C}\). What are the magnitude and direction of the electric field at \((a)(4.00
(a) Plot the value of the radial component of the electric field due to a positively charged pellet as a function of distance from the pellet center. (b) Repeat for a negatively charged pellet. Take
An electron initially placed \(0.10 \mathrm{~m}\) to the right of a small charged sphere moves to the right with an inirial acceleration of \(4.0 \times 10^{7} \mathrm{~m} / \mathrm{s}^{2}\). What is
A small sphere carrying \(6.0 \mathrm{nC}\) of charge is placed \(100 \mathrm{~mm}\) from a small sphere carrying \(3.0 \mathrm{nC}\) of charge. Assume the spheres are tiny relative to the
Two beads, one carrying charge \(+q\) and the other carrying charge \(+4 q\), are separated by a distance \(d\) that is much greater than the radius of each bead. (a) Is there any location along the
In an inkjet printer, tiny drops of ink of inertia \(m\) are given a charge \(q\) and then fired toward the paper at speed \(v\). They first pass between two charged plates of length \(\ell\) that
(a) What electric field magnitude is needed to balance the gravitational force exerted by Earth on an electron near Earth's surface? \((b)\) Relative to the electron's position, where would you have
Consider a rectangle with diagonal length \(2 a\) in the \(y z\) plane with the origin at the center of the rectangle. Four beads, each carrying charge \(q\), are placed on the rectangle perimeter,
A particle carrying a charge of \(6.0 \mu \mathrm{C}\) is located at the origin of a rectangular coordinate system, and a particle carrying a charge of \(4.0 \mu \mathrm{C}\) is located at \((0,5.0
Five charged particles are located around a semicircular arc of radius \(100 \mathrm{~mm}\), with one particle at each end of the semicircle and the remaining three spaced equally between the two
A positively charged particle 1 is at the origin of a Cartesian coordinate system, and there are no other charged objects nearby. You need the electric field magnitude at the position \((3.00
Three particles carrying equal positive charge \(q\) are located at the corners of an equilateral triangle with side length \(a\). What are the magnitude and direction of the electric field \((a)\)
Two nonconducting spheres 1 and 2 carry the same charge, and the magnitude of the electric force exerted by each sphere on the other is \(0.10 \mathrm{~N}\) when they are \(50 \mathrm{~mm}\) apart.
A particle carrying a charge of \(-5.0 \mu \mathrm{C}\) is located at the origin of a rectangular coordinate system, and a particle carrying a charge of \(12.0 \mu \mathrm{C}\) is located at \((1.0
In table salt-sodium chloride, \(\mathrm{NaCl}-\) the \(\mathrm{Na}^{+}\)and \(\mathrm{Cl}^{-}\) ions are arranged in a cubic crystal structure. You can observe in this structure a cube made up of
A water molecule (Figure P23.43) has a dipole moment of \(6.19 \times 10^{-30} \mathrm{C} \cdot \mathrm{m}\). If the \(\mathrm{O}-\mathrm{H}\) bonds were ionic bonds (in reality they are polar
Two plastic bowling balls, 1 and 2 , are rubbed with cloth until they each carry a uniformly distributed charge of magnitude \(0.10 \mathrm{nC}\). Ball 1 is negatively charged, and ball 2 is
As Figure P23.43 shows, the water molecule is bent, and the angle formed by the three atoms is \(104.5^{\circ}\). Given that the permanent dipole moment of the molecule is \(6.186 \times 10^{-30}
A proton located several proton diameters away from a small charged object carrying charge \(q\) is subject to an electric field of magnitude \(E\). As the proton moves a distance \(d\) along the
A dipole consisting of a proton and an electron held a distance \(d\) apart is aligned along a \(z\) axis. A second proton is then placed at the midpoint of the line joining the electron and proton
Equation 23. 12,\[E_{y}=k \frac{q_{\mathrm{p}}}{y^{2}}\left[\left(1-\frac{d}{2 y}\right)^{-2}-\left(1+\frac{d}{2 y}\right)^{-2}\right]\]was derived for the case \(y>d / 2\). Fxplain why this equation
An electric quadrupole can be constructed by placing four charged objects at the corners of a square (Figure P23.49). The objects are identical except for the charge they carry: The two objects in
A dipole is centered at the origin of a coordinate system, and a small charged sphere is some distance away along the perpendicular bisector of the dipole. The particle carries a uniformly
Two thin plastic rods, each of length \(\ell\), are joined end to end. One rod is positively charged with a uniform linear charge density \(\lambda\), and the other carries a negative charge density
An electric dipole that has dipole separation \(d\) is aligned along the \(y\) axis of an \(x y\) coordinate system, pointed in the positive \(y\) direction. (a) Show that for \(x\) and \(y\) much
You've been given the task of charging a spherical weather balloon made of a conducting material, and you want to put as much charge on it as possible. An experienced colleague advises you that the
A positively charged particle is released from rest along the axis of symmetry of a fixed ring carrying a uniformly distributed negative charge. Describe the motion of the particle.
A uniformly charged rod lies along the \(z\) axis of an \(x y z\) coordinate system, from \(z=-100 \mathrm{~mm}\) to \(z=+100 \mathrm{~mm}\). The linear charge density on the rod is \(100 \mathrm{nC}
In the uniform charge distribution shown in Figure P23.56, each of the three arcs forms one-fourth of the circumference of a ring. The upper right and lower left arcs each carry a positive charge
The thin glass rod of length \(\ell\) in Figure P23.57 has a linear charge density that starts out as zero at the left end of the rod and increases linearly from left to right. The positive charge on
You have two disks, 1 and 2 , both of radius \(R=25.0 \mathrm{~mm}\) and both made of the same nonconducting material. Disk 1 carries a uniformly distributed charge \(q_{1}=1.50 \mu \mathrm{C}\), and
What percentage error in the electric field magnitude do you introduce by approximating the charged disk of Figure 23. 29 as an infinite charged sheet with the same surface charge density for (a)
You wish to determine the electric field magnitude along the perpendicular bisector of a \(250-\mathrm{mm}\) line along which \(30 \mathrm{nC}\) of charge is distributed uniformly. You want to get by
For a uniformly charged disk of radius \(90 \mathrm{~mm}\), you wish to determine the electric field magnitude along the axis that runs through the disk center and perpendicular to the disk face. You
Three narrow concentric rings of radii \(50 \mathrm{~mm}, 70 \mathrm{~mm}\), and \(90 \mathrm{~mm}\) are centered about the origin, with the axis of symmetry of each ring oriented along the \(y\)
Two large oppositely and uniformly charged parallel plates are separated by \(10 \mathrm{~mm}\). An electron is projected halfway between the plates and parallel to them with an initial speed of
A particle of inertia \(m\) that carries charge \(q\) is held above an infinite sheet on which the surface charge density is \(\sigma\). The charge on the sheet is of the same type as the charge on
A uniformly charged thin rod lies along the \(x\) axis from \(x=0\) to \(x=+\infty\). (a) Derive an expression for the component \(E_{y}\) of the electric field in the positive \(y\) direction, and
One half of a charged thin ring of radius \(R\) carries a charge \(q_{1}\) uniformly distributed over it, and the other half of the ring carries a charge \(q_{2}\) uniformly distributed over it. For
In Figure P23.67, determine the \(x\) and \(y\) components of the electric field at position \(\mathrm{P}\), which is a distance \(d\) above onc end of a rod of length \(\ell\) carrying uniformly
A thin rod of length \(2 \ell\) has a linear charge density that is \(\lambda_{0}\) at the left end but decreases linearly with distance going from left to right in such a way that the charge on the
You place \(2.2 \mu \mathrm{C}\) of charge along a long nonconducting rod. The rod extends from \(x=0\) farther than you can see along the positive \(x\) axis. The charge distribution has the form of
The water molecule is a permanent dipole with a dipole moment of \(6.186 \times 10^{30} \mathrm{C} \cdot \mathrm{m}\). If a single water molecule were oriented such that its dipole moment is along
A microwave oven, which fills the oven chamber with oscillating electric fields, works well at heating food that has a high water content. However, it does not work well with frozen food or with food
The electric force due to a uniform external electric field causes a torque of magnitude \(10.0 \times 10^{-9} \mathrm{~N} \cdot \mathrm{m}\) on an electric dipole oriented at \(30^{\circ}\) from the
A dipole is to be released in a region where there is a uniform electric field and no dissipative forces. Describe the motion of the dipole if it is released from rest in an orientation \((a)\)
A small object with dipole moment \(p\) is released near its equilibrium orientation in a uniform electric field of magnitude \(E\). The rotational inertia of the dipole is \(I\). (a) What is the
A dipole that is free to move is placed near a fixed dipole, with the midpoint of the free dipole on the perpendicular bisector of the fixed dipole. The distance from the free dipole to the fixed one
In a particular region of space, an electric field has a constant direction but its magnitude increases smoothly along that direction. A dipole is placed in this field, its dipole moment is oriented
A particle carrying \(5.0 \times 10^{-7} \mathrm{C}\) of charge is located on the perpendicular bisector of a small dipole, \(300 \mathrm{~mm}\) from the center of the line joining the two poles of
There are two possible alignments of a dipole in an external electric field where the dipole is in equilibrium. (a) Draw a field diagram for a uniform electric field and show these two alignments.
In very rare cases, the polarizability of a molecule may be negative. (a) Draw a picture showing the resultant charge distribution when such a molecule is placed in the electric field surrounding a
Two identical particles, each carrying charge \(q\), are a distance \(r\) apart. A dipole for which the dipole moment magnitude is \(p\) and the dipole separation is \(d
An electrically neutral molecule is collinear with (and located between) two charged particles, one carrying a charge of \(+3.56 \mu \mathrm{C}\) and the other carrying a charge of \(-1.05 \mu
Express the SI unit of electric field in terms of joules and other SI base units.
Four particles are located at the corners of a square that is \(50 \mathrm{~mm}\) on a side. All four particles carry a charge of magnitude \(3.0 \mathrm{nC}\), with positive charge at the lower left
Each of the two particles in Figure P23.85 carries a charge of magnitude \(q\). Determine a position, if one exists, where the electric field magnitude is zero if the charge \((a)\) is of the same
An electron is launched into a region of constant electric field, \(\vec{E}=2 \times 10^{4} \mathrm{~N} / \mathrm{C}\) directed along the positive \(y\) axis of a rectangular coordinate system, with
An electrically neutral, linear, polar molecule has positive charge equivalent to the charge on one proton centered \(0.30 \mathrm{~nm}\) from its center of mass and an equal quantity of negative
You have a pair of objects that interact with each other electrically. The objects initially are separated by a distance \(r\) and exert a force of magnitude \(F^{F}\) on each other. If the
A particle carrying a charge of \(+32.0 \mathrm{nC}\) is located at \((10.0 \mathrm{~nm}, 95. 0 \mathrm{~nm})\), and a particle carrying a charge of \(+98.0 \mathrm{nC}\) is located at \((45.0
Figure P23.90 shows four charged particles, each having a charge equal to \(+3.00 \mu \mathrm{C}\), arranged in a square. What are the magnitude and direction of the electric field at \(\mathrm{P}\),
A uniformly charged rod extends from \(y=-150 \mathrm{~mm}\) to \(y=+150 \mathrm{~mm}\) along the \(y\) axis of an \(x y\) coordinate system. The charge on the rod is \(30 \mathrm{nC}\). (a) With the
A small sphere 1 carrying charge \(q_{1}\) and having inertia \(m_{1}\) is constrained to moving inside a narrow vertical tube (Figure P23.92). Fixed at the bottom of the tube is a small sphere 2
Your boss is designing a new data storage system that will have a lot of dipoles very close to one another. They will point in the \(z\) direction and be closely spaced in the \(x\) and \(y\)
You are designing a new guidance mechanism for an inkjet printer. You believe that a circular arc of charge, mounted in the \(x y\) plane, is needed in order to deflect the ink droplets most
A rod of length \(\pi R\) is composed of three nonconducting segments of equal length. The middle segment is electrically neutral, and each end segment carries a uniformly distributed negative charge
Draw a field line diagram for an infinite plate that carries a uniform positive charge distribution inside the plate.
Consider the field line diagram shown in Figure 24.7. (a) What are the signs of the charges on the two small spherical objects? (b) What are the relative magnitudes of these charges? (c) What is the
Consider the three-dimensional dipole field line diagram shown in Figure 24.10. Six field lines emanate from the positively charged end, and six terminate on the negatively charged end.(a) What is
An electrically neutral, conducting sphere contains an irregularly shaped cavity. Inside the cavity is a particle carrying a positive charge \(+q\). What are the sign and magnitude of the charge on
Consider a cylindrical Gaussian surface of radius \(r\) and length \(\ell\) in a uniform electric field \(\vec{E}\), with the length axis of the cylinder parallel to the electric field (Figure
Consider a charged sphere of radius \(R\) carrying a positive charge \(q\) that is uniformly distributed over the volume of the sphere. What is the magnitude of the electric field a radial distance
What is the electric field magnitude a radial distance \(r\) from the central length axis of an infinitely long thin rod carrying a positive charge per unit length \(\lambda\) ?
What is the electric field a distance \(d\) from a thin, infinite nonconducting sheet with a uniform positive surface charge density \(\sigma\) ?
In Figure 24. 19, which of the two charged spheres carries a charge of greater magnitude?Data from Figure 24. 19 E A B C
Consider Gaussian surfaces 1-3 in Figure 24. 19. Determine the field line flux through each surface (considering just the two dimensions shown).Data from Figure 24. 19 E A B C
In Figure 24. 19 , is the field line density greater at point A or point B? At which of these locations is the magnitude of the electric field greater? Is the field line density at point C zero or
The electric field lines in Figure 24. 20 tell you there must be one or more charged particles inside the Gaussian surface defined by the dashed line. Could the electric field shown be due to a
Figure 24. 21 shows a small ball that carries a charge of \(+q\) inside a conducting metal shell that carries a charge of \(+2 q\).(a) What are the sign and magnitude of the charge on the inner
Suppose a charged particle is located at the origin. What is the direction of the electric field at the point \((0.6,1.2)\) if the particle is \((a)\) positively charged and \((b)\) negatively
Because of the presence of positively charged ions in Earth's atmosphere, on a calm day free electrons (that is, electrons not bound to atoms) just above Earth's surface generally experience a small
Can you draw an electric field line through a location in space where the electric field magnitude is zero?
You and a friend are asked to draw the two-dimensional electric field line partern for two charged objects located near each other. The charge on the first object is \(+2 q\) (with \(q\) positive),
A positively charged test particle is released from rest in a uniform electric field. The only force experienced by the particle is the clectric force in that ficld. (a) Describe the trajectory the
A certain field line diagram illustrates the electric field due to three particles that carry charges \(5.0 \mu \mathrm{C},-3.0 \mu \mathrm{C}\), and \(-2.0 \mu \mathrm{C}\). If 20 field lines
Figure \(\mathrm{P} 24. 7\) shows the electric field produced by an electric dipole. How would a positively charged test particle begin to move when released from rest \((a)\) at point \(A\), (b) at
Two particles of charge \(+q\) are located at opposite ends of one diagonal of a square, and two particles of charge \(-q\) are located at opposite ends of the square's other diagonal. Sketch the
Assume that a test particle is released from rest in an electric field and experiences no forces other than the electric force exerted by that electric field. Does an electric field line passing
Draw several field lines surrounding the three charged particles shown in Figure P24.10.Data from Figure P24.10 Figure P24.10 +q -29 +q
Two classmates sitting next to you have made an electric field diagram. You are looking at it (not during a test) to see if they did it correctly, but part of the diagram is covered by a quarter, as
Outline an algorithm for a computer program that traces out the electric field lines surrounding a charged object. Assume that functions have already been provided to draw the charged object itself
There are many parallels between gravitational phenomena and electrical phenomena: One can think of a test object with mass in a gravitational field as analogous to a test object with positive charge
A small charged ball is suspended at the center of a spherical balloon that is nestled snugly inside a cubical cardboard box. On one side, the balloon touches the wall of the box. (a) At this point
Where in Figure P24.15 other than around the point charge is the electric field greatest in magnitude?Data from Figure P24.15 Figure P24.15
Suppose a certain planar surface has 2000 field lines passing through each square meter, normal to the surface. How many field lines pass through each square meter if the surface is tilted by
Consider the pattern of five field lines shown in Figure P24.17. Rank positions A, B, and C according to the magnitude of their electric fields, from greatest to smallest.Data from Figure P24.17 A B.
Make a geometric argument, based on how the field lines spread out into space, that the magnitude of the electric field surrounding a long, straight, charged wire is proportional to \(1 / r\), where
Make a geometric argument, based on the pattern of electric field lines, that the magnitude of the electric field surrounding a large, flat, charged metal plate is constant and independent of the

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