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Weighing an Object Immersed in a Fluid A solid sphere of density 3.00 × 103 kg/m3 hangs from a spring scale (Scale 1) that reads 200.0 N. A large cylindrical beaker with inside diameter 40.0 cm and partially filled with water sits on Scale 2, which reads 1000 N. The sphere is then lowered into the water until it is fully immersed but not touching the beaker (Figure 12-31). Assume that no water is spilled from the beaker. What are the new readings on the two scales?
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Atomic Physics
Work over a Closed Path in an Electric Field As shown in Figure 21-2, a positive point charge (Q)produces an electric field. This electric field points radially outward, with an electric field strength that varies inversely with the square of radial distance, as we saw in Chapter 19. Now consider a closed path ABCDA (Figure 21-2). Show that the total work done by an external agent (henceforth we will simply call it an agent) in moving a small positive test charge q around the closed path is zero. By external agent we mean someone exerting the required forces to move the charge with negligible acceleration along the indicated path in the electric field. We are assuming that we can neglect forces other than electrical. We need the assumption that the speed is infinitesimal, so no work goes into a change in kinetic energy. Assume that charge Q is fixed in position.
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Atomic Physics
Electrical Potential Energy for Four Charges Find the total work required to move four charges (+2.00 nC,+3.00 nC,+4.00 nC,+5.00 nC) from initial positions infinitely far apart to the corners of a square with sides of 0.150 m, as shown in Figure 21-6. Define the zero of electrical potential energy to be when the charges are infinitely far apart. What is the electrical potential energy of the charge configuration shown in Figure 21-6?
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Atomic Physics
Charged Particle Speed Consider the situation shown in Figure 21-7. Initially, a negative charge q2 of mass m is at a distance r2 from a fixed in position positive charge q1. At this position q2 was given a speed of v_0 in a direction directly toward q1. What is the speed of q2 when it reaches a smaller distance, r1, from q1? Is the speed of charge q2 more or less when it moves to r1? If the charge had the same initial speed v_0but in the opposite direction (away from q1), how would the answer to (a) be different? Justify your response. You can assume that changes in gravitational potential energy are negligible.
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Atomic Physics
Electric Potential for Three Charges Find the electric potential at point P in Figure 21-8. How much work is required to move a a+1.00 μC charge to point P from an infinite distance?
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Atomic Physics
Work to Move Charge A particle has a positive charge of 3.00 nC and a mass of 3.07×〖10〗^(-23) kg. Initially it is at rest at a point at an electric potential of-12.0 V. How much work is required to move it to another point that is at an electric potential of +36.0 V? Assume that it moves in a horizontal plane so that there is no change in gravitational potential energy, and no other forces are present.
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Atomic Physics
Electric Potential for a Charged Plastic Washer A thin plastic washer (non-conducting) has an inner radius of 2.00 cm and an outer radius of 3.00 cm. It is uniformly charged with surface charge density σ=240 nC/m^2. What is the electric potential at a point h = 4.00 cm directly above the centre of the washer (point P in Figure 21-12)?
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Atomic Physics
Proton Beam Therapy TRIUMF can produce protons with energies between 5 MeV and 120 MeV in the lower energy beam (called BL2C). Consider a beam of 100 MeV protons used for treating cancer. What is the energy of one of these protons, in joules? The energy of the protons is built up after many passes through an accelerating potential of 94.0 kV. How many passes are needed to produce 100 MeV protons? The protons are accelerated by an electric potential difference across a gap between two halves of the cyclotron chamber. Which side of this acceleration region has the higher electric potential?
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Atomic Physics
