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physics
particle physics

Questions and Answers of Particle Physics

Two capacitors, A and B, are each connected to a 9-V battery. If \(C_{\mathrm{A}}>C_{\mathrm{B}}\), which capacitor stores the greater amount of charge?
The plate spacing in a typical parallel-plate capacitor is about \(50 \mu \mathrm{m}\). (a) What is the plate area in a \(1-\mu \mathrm{F}\) capacitor? (b) Given that the electric field at which
Coaxial cables used for cable television typically have a central metallic core of \(0.20-\mathrm{mm}\) radius, surrounded by a cylindrical metallic sheath of \(2.0-\mathrm{mm}\) radius. The two are
(a) To calculate the "capacitance" of an isolated sphere, evaluate the result we obtained in Example 26.4 in the limit that \(R_{2}\) goes to infinity.(b) What is the capacitance of the spherical
A \(1.0-\mu \mathrm{F}\) parallel-plate capacitor with a plate spacing of \(50 \mu \mathrm{m}\) is charged up to the breakdown threshold. (a) If the electric field in the air between the capacitor
A parallel-plate capacitor has plates of area \(A\) separated by a distance \(d\). The magnitude of the charge on each plate is \(q\). (a) Determine the magnitude of the force exerted by the
To store electric potential energy, the flash unit on a typical camera uses a \(100-\mu \mathrm{F}\) capacitor charged to a potential difference of \(300 \mathrm{~V}\). When the flash is fired, the
(a) In Figure 26.29, what is the magnitude of \(q_{\text {bound }}\) ? Express your answer in terms of \(q_{0}\) and the properties of the dielectric.(b) What is the bound surface charge density on
Verify that in the solution to part \(a\) of Example 26.6,(a) the ratio of units \(\mathrm{C}^{2} /(\mathrm{N} \cdot \mathrm{m})\) is equivalent to the unit \(\mathrm{F}\) and \((b)\) the product of
Show that, if you account for the free and bound charges, Gauss's law in vacuum (Eq. 24.8) yields the same result for the electric field outside the insulation as Gauss's law in matter (Eq. 26.25)
Suppose both particles in Figure \(25.2 b\) are released from rest. Let \(m_{2}>m_{1}\) and consider only electric interactions. (a) How do their kinetic energies compare after they have both
As the dipole in Figure 25.3 continues to rotate, it reaches the point where its axis is aligned with the electric field of the massive object. (a) What happens to the electric potential energy as
(a) Suppose the particle in Figure 25.4 moves along the \(x\) axis from point \(\mathrm{A}\) at \(x=x_{\mathrm{A}}\) to point \(\mathrm{B}\) at \(x=x_{\mathrm{B}}\). How much work is done by the
Suppose the electrostatic work done on a charged particle as it moves along the gray path from \(A\) to \(C\) in Figure \(25.6 c\) is \(W\). What is the electrostatic work done on the particle(a)
(a) If the electrostatic work done on a charged particle as it moves around a closed path is zero, does this also mean that the electrostatic work done on the particle is zero as it moves along a
(a) Is the potential difference along any path from A to \(\mathrm{C}\) in Figure \(25.6 c\) positive, negative, or zero? \((b)\) Along any path from \(\mathrm{C}\) to \(\mathrm{B}\) ? (c) Along the
Consider a single charged particle. Are there any equipotential lines or equipotential surfaces surrounding this particle?
When you hold a positively charged rod above a metallic sphere without touching it, a surplus of negative charge carriers accumulates at the top of the sphere, leaving a surplus of positive charge
(a) Using Eq. 25.5, determine whether the electrostatic work done on particle 2 along path CB in Figure 25.15 is positive, negative, or zero. (b) Does moving the particle carrying charge \(q_{2}\)
Suppose we keep particle 2 stationary and move particle 1 in so that their final separation is the same as that in Figure 25.15. Is the electrostatic work done on particle 1 as it is moved in also
Suppose the charged particles in Figure 25.16 are assembled in a different order-say, 3 first, then 1 , and finally 2 . Do you obtain the same result as in Eq. 25.13 and Eq. 25.14? Figure 25.16 To
(a) Using Eq. 25.20, determine whether the potential difference between A and B in Figure 25.17 is positive, negative, or zero.(b) From the directions of the electric force and the force
Verify that Eq. 25.25 is consistent with Eq. 25.20 by substituting the expression for the electric field of a charged particle.Equations -W12(AB) 91 1 VAB 92 4TED B TA (25.20)
Describe how the potential varies as you go around the closed path in Figure 25.22 in the direction shown, starting from a potential \(V_{\mathrm{P}}\) at \(\mathrm{P}\). Figure 25.22 The
Verify that the potentials obtained in Examples 25.6 and 25.7 have the correct sign.Data from Example 25.6A thin rod of length \(\ell\) carries a uniformly distributed charge \(q\). What is the
Apply Eq. 25.40 to the potential you obtained for the uniform field between two parallel charged plates in Example 25.5, and verify that you get the correct expression for the electric field between
Calculate the electric field at any point on the axis of a thin charged disk from the potential we obtained in Example 25.7. Compare your answer to the result we obtained by direct integration.Data
A point charge \(q_{1}=+5.70 \mu \mathrm{C}\) is fixed at the origin of a coordinate plane. How much electrostatic work is done by the electric force on a second point charge \(q_{2}=-3.40 \mu
A pair of electrons is fixed at certain positions \(\left(e_{1}\right.\) at the origin while \(e_{2}\) is at point \(a\) ) and carries an electric potential energy of \(4.8 \times 10^{-5}
Points \(A\) and \(B\) are on the same electric field line. If an electron is released and moves from A to \(\mathrm{B},\) (a) is the field directed from \(A\) to \(B\) or from \(B\) to \(A\) ? (b)
Particle A, located at the origin, carries a charge of \(6.0 \mathrm{nC}\).(a) What is the electrostatic potential (relative to zero potential at infinity) at a position \(r=8.0 \mathrm{~cm}\) from
An electron is released from rest in a uniform electric field of magnitude \(4.0 \times 10^{3} \mathrm{~N} / \mathrm{C}\). What is the electrostatic work done by the electric field on the particle
An electron and a proton are fixed at the vertices of an equilateral triangle with sides of length \(a\). (a) What is the potential (relative to zero at infinity) at the apex of the triangle. \((b)\)
Six particles, each carrying a charge of \(2.0 \mathrm{nC}\), are equally spaced along the equator of a sphere that has a radius of \(0.40 \mathrm{~m}\). What is the electrostatic potential (relative
An electron and a proton are held \(2 \mathrm{~m}\) apart. The midpoint between the electron and the proton sets the origin of a coordinate system, with the \(x\) axis pointing toward the proton.(a)
(a) What is the potential at a point \(50 \mathrm{~cm}\) away from a point charge with a magnitude of \(3.0 \mathrm{nC}\) ?(b) How would the potential change if you measure the potential at a point
A conducting sphere with a diameter of \(8.00 \mathrm{~cm}\) carries a charge of \(3.5 \mathrm{nC}\) that is uniformly distributed. Calculate(a) the surface charge density of the sphere (b) the
Two point charges \(q_{1}=+\mathrm{Q}\) and \(q_{2}=-3 \mathrm{Q}\) are placed along the \(x\)-axis, \(10 \mathrm{~cm}\) apart \(\left(q_{1}\right.\) at the origin, \(q_{2}\) at \(x=+10
A particle carrying charge \(+10.00 \mathrm{nC}\) sets the origin of a rectangular coordinate system. Taking the electrostatic potential to be zero at infinity, locate the distance from the origin of
A positively charged infinite sheet has a surface charge density of \(+5.0 \mathrm{nC} / \mathrm{m}^{2}\). What is (a) the electric field at a distance \(0.10 \mathrm{~m}\) from the sheet and (b)
An infinite sheet has a uniform positive surface charge. Points A and B are located at distances of \(5.0 \mathrm{~cm}\) and \(10.0 \mathrm{~cm}\) from the sheet, respectively.(a) Is the potential
Two parallel conducting plates are \(0.10 \mathrm{~m}\) apart and carry equal and opposite charges. They are large enough relative to the \(0.10-\mathrm{m}\) separation distance that we can assume
A thin disk of radius \(R=5 \mathrm{~cm}\) has uniform surface charge density \(\sigma=8 \mathrm{nC} / \mathrm{m}^{2}\). Calculate the potential (relative to zero at infinity) on the axis that runs
A point charge \(q=+5 \mathrm{nC}\) is at the center of a thick conducting spherical shell of internal radius \(10 \mathrm{~cm}\) and external radius \(12 \mathrm{~cm}\).(a) What is the magnitude and
An infinitely long positively charged wire has a linear charge density \(\lambda=3 \mathrm{nC} / \mathrm{m}\). Calculate the electrostatic potential at distances of(a) \(1.0 \mathrm{~m},\)(b)
A particle carrying a charge of \(6 \mathrm{nC}\) is at the center of a thick conducting spherical shell of inner radius \(9 \mathrm{~cm}\) and outer radius \(10 \mathrm{~cm}\).(a) What is the
At point \(\mathrm{A}\) in Figure 34. 28 , do the waves from the two slits add or cancel?Data from Figure 34. 28 A
If the two sets of fringes shown in Figure 34. 29 were produced by the same diffraction grating, which set is the product of the longer-wavelength radiation?Data from Figure 34. 29
Coherent light of wavelength \(\lambda\) is normally incident on two slits separated by a distance \(d\). What is the greatest possible fringe order?
Given the relationship between the energy \(E\) of a photon and its frequency \(f\) and the de Broglie expression relating momentum \(p=m v\) and wavelength \(\lambda\), determine the ratio \(E / p\)
Do you expect to be able to observe the diffraction of light through \((a)\) the front door to your house; \((b)\) the holes in a button; (c) the gaps between threads of the fabric of an umbrella?
Coherent green light of wavelength \(530 \mathrm{~nm}\) passes through two very narrow slits separated by \(1.00 \mu \mathrm{m}\). What is \((a)\) the angular location of the first-order bright
Figure 34.21 shows diffracted \(\mathrm{x}\)-ray intensity as a function of the Bragg angle \(\alpha\), obtained using \(\mathrm{x}\) rays having a wavelength of \(0.11 \mathrm{~nm}\). (a) Without
Calculate the de Broglie wavelength associated with \((a)\) a \(0.14-\mathrm{kg}\) baseball thrown at \(20 \mathrm{~m} / \mathrm{s}\) and \((b)\) an electron of mass \(9.1 \times 10^{-31}
A 50 -W incandescent light bulb emits about \(5.0 \mathrm{~W}\) of visible light. (The rest is converted to thermal energy.) If a circular aperture \(5.0 \mathrm{~mm}\) in diameter is placed \(1.0
An astronomer wishes to determine the relative heights of the intensity peaks for the bright fringes produced by two wavelengths of radiation emitted by sodium atoms. The wavelengths are \(589.0
Eyeglass lenses made of crown glass \((n=1.52)\) are given a thin coating of magnesium fluoride \((n=1.38)\) to minimize reflection of light from the lens surface. What is the minimum coating
Consider the diffraction pattern shown actual size in Figure 34.40. If the pattern was formed by light from a \(623-\mathrm{nm}\) (red) laser passing through a single narrow slit and the screen on
A magnifying glass that has a focal length of \(0.25 \mathrm{~m}\) and a diameter of \(0.10 \mathrm{~m}\) is used to focus light of wavelength \(623 \mathrm{~nm}\). (a) What is the radius of the
The width of one pixel in the sensor for a digital camera is about \(2.0 \mu \mathrm{m}\). If the camera lens has a diameter of \(40 \mathrm{~mm}\) and a focal length of \(30 \mathrm{~mm}\), is the
Light of wavelength \(380 \mathrm{~nm}\) strikes the metal target in Figure 34.47. As long as the potential difference \(V_{\mathrm{CT}}\) between the target and the collector is no greater than
Name some characteristics that allow you to observe light diffraction.
Which wavelength of electromagnetic radiation do you expect to be diffracted by a window screen? What is the frequency of this radiation?
Planar waves from a monochromatic light source are normally incident on a circular obstacle, which casts a shadow on a screen positioned behind the obstacle. What do the wave properties of light
Light of wavelength \(\lambda\) is incident on an aperture of width \(a\), producing diffraction. Describe the change(s) in the diffracted waves \((a)\) when the aperture width is doubled and \((b)\)
A friend is standing behind a large tree and yelling. You can hear him, but not see him. Why?
Coherent green light of wavelength \(530 \mathrm{~nm}\) passes through two narrow slits for which the center-to-center separation distance is \(100 \mu \mathrm{m}\). What is the difference in phase
A diffraction grating has adjacent slits separated by \(4.00 \mu \mathrm{m}\). When yellow light \((\lambda=589 \mathrm{~nm})\) is incident on the grating, what are the angular positions of the
You shine a red laser beam on a diffraction grating and then shine a green laser beam on the grating. Is the spacing of the bright fringes for the red beam greater than, smaller than, or equal to the
A reflection diffraction grating of width \(w\) has \(N\) grooves and is illuminated by normally incident monochromatic light. What condition determines how many orders of constructive interference
Violet light \((\lambda=400 \mathrm{~nm})\) passing through a diffraction grating for which the slit spacing is \(6.0 \mu \mathrm{m}\) forms a pattern on a screen \(1.0 \mathrm{~m}\) away from the
Light passing through a two-slit grating makes a pattern on a screen located \(500 \mathrm{~mm}\) away. In this pattern, the fifth-order dark fringe is \(45.0 \mathrm{~mm}\) from the central bright
A diffraction grating casts a pattern on a screen located a distance \(L\) from the grating. The central bright fringe falls directly in the center of the screen. For the highestorder bright fringe
(a) For the two-slit barrier shown in Figure P34.13, calculate the angle \(\theta_{1}\) for the first-order bright fringe if the slit separation distance is \(d_{\text {orig }}=1.0 \mu \mathrm{m}\)
Why are \(\mathrm{x}\) rays rather than visible light used to determine structure in crystals?
Do the bright spots in an \(\mathrm{x}\)-ray diffraction pattern get closer together, get farther apart, or not change position when the energy of the \(\mathrm{x}\) rays is doubled?
A monochromatic \(x\)-ray beam that has a wavelength of \(1.000 \times 10^{-10} \mathrm{~m}\) strikes a sodium chloride crystal that has a lattice spacing of \(2.815 \times 10^{-10} \mathrm{~m}\).
In an x-ray diffraction experiment on a crystal that has a cubic lattice, the greatest Bragg angle at which you see a peak in the intensity of diffracted \(x\) rays is \(35.00^{\circ}\). If the
You are doing x-ray diffraction on a crystal that has a cubic structure, using \(0.500-\mathrm{nm} x\) rays. If the lattice spacing is \(d=6.70 \times 10^{-10} \mathrm{~m}\), what are the two
What is the order of magnitude of the de Broglie wavelength of a person walking down the street?
How fast must a proton move in order to have the same de Broglie wavelength as the electron in Example 34. 4, \(1.5 \times 10^{-10} \mathrm{~m}\) ?Data from Figure P34.13ddd
A narrow solid obstacle is placed in the path of the electron in Figure P34.21. Does the electron have a chance of reaching the detector?Data from Figure P34.21 electron detector obstacle
What is the de Broglie wavelength of a \(0.17-\mathrm{kg}\) hockey puck moving at \(45 \mathrm{~m} / \mathrm{s}\) ?
An alpha particle, which consists of two neutrons and two protons, has a mass of \(6.645 \times 10^{-27} \mathrm{~kg}\) and a charge of \(2 e\). What is the de Broglie wavelength of an alpha particle
Rank the following types of radiation and types of particles in order of increasing spacing between bright fringes in their diffraction patterns: yellow light, blue light, electrons moving at a speed
You are accelerating electrons toward a diffraction grating to produce a diffraction pattern. If you want the pattern to contain 101 bright fringes and the spacing between slits in the grating is
Which photons contain more energy: those of blue light or those of red light?
In a region of Earth's surface where the average amount of solar energy striking a square meter of ground each second is \(200 \mathrm{~J}\), how many photons strike each square meter each second?
What is the smallest amount of \((a)\) momentum and (b) energy that can be delivered using red light for which \(\lambda=700 \mathrm{~nm}\) ?
At what rate do photons emitted by a green-light laser \((\lambda=532 \mathrm{~nm})\) hit a wall \(2.00 \mathrm{~m}\) from the laser if the power rating is \(5.00 \mathrm{~mW}\) ? What assumption
The sun has a power output of \(3.83 \times 10^{26} \mathrm{~W}\). (a) How many photons does the Sun emit each second? What assumption(s) must you make to answer this question? (b) Installed on your
(a) What is the energy of a 633-nm photon? (b) Two helium-neon lasers both emit 633-nm photons. Laser A has a power rating of \(1.0 \mathrm{~mW}\), but laser \(\mathrm{B}\) has a power rating of only
Near the center of a diffraction pattern, adjacent maxima are separated by a distance of \(20 \mathrm{~mm}\). The diffraction grating is \(0.200 \mathrm{~m}\) from the screen and has a slit spacing
A red laser beam \((\lambda=650 \mathrm{~nm})\) is sent through a double slit to a screen that is \(400 \mathrm{~mm}\) wide and \(1.00 \mathrm{~m}\) away from the slits. (a) If the separation
Laser light passes through a double-slit barrier with slit separation \(d=0.150 \mathrm{~mm}\) onto a screen a distance \(L=5.00 \mathrm{~m}\) away. The distance between the central and first-order
Using a diffraction grating with 200 slits \(/ \mathrm{mm}\) to create a diffraction pattern on a screen \(2.00 \mathrm{~m}\) away from the grating, you see bright fringes \(170 \mathrm{~mm}\) apart.
Green light \((\lambda=510 \mathrm{~nm})\) shines through two slits separated by \(2.30 \times 10^{-6} \mathrm{~m}\). The resulting diffraction pattern is cast on a screen \(450 \mathrm{~mm}\) away.
The radiation emitted by mercury vapor lamps includes green 546. 1-nm light and blue 435. 8-nm light. If this radiation passes through a transmission grating that has 600 slits/mm to form a
Cell phone radiation has a wavelength of about \(300 \mathrm{~mm}\). You are in the lobby of an office building in which the façade is a series of large, multistory panes of glass separated by
You pass \(589.0-\mathrm{nm}\) radiation and \(589.6-\mathrm{nm}\) radiation through a diffraction grating that has 500. 0 slits \(/ \mathrm{mm}\). (a) In the diffraction pattern, what is the angular

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