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A uranium nucleus (mass 238 u, charge 92e) decays, emitting an alpha particle (mass 4 u, charge 2e) and leaving a thorium nucleus (mass 234 u, charge 90e). At the instant the alpha particle leaves the nucleus, the centers of the two are 4.5 fm apart and essentially at rest. Find their speeds when they're a great distance apart. Treat each particle as a spherical charge distribution. The answers of va and vTh should be in m/s.
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- A Figure P23.65 shows two identical conducting spheres, each with charge q, suspended from light strings of length L. If the equilibrium angle the strings make with the vertical is , what is the mass m of the spheres? Figure P23.65A circular ring of charge with radius b has total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring? (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) none of those answersIn Figure P24.49, a charged particle of mass m = 4.00 g and charge q = 0.250 C is suspended in static equilibrium at the end of an insulating thread that hangs from a very long, charged, thin rod. The thread is 12.0 cm long and makes an angle of 35.0 with the vertical. Determine the linear charge density of the rod. FIGURE P24.49
- A Two positively charged particles, each with charge Q, are held at positions (a, 0) and (a, 0) as shown in Figure P23.73. A third positively charged particle with charge q is placed at (0, h). a. Find an expression for the net electric force on the third particle with charge q. b. Show that the two charges Q behave like a single charge 2Q located at the origin when the distance h is much greater than a. Figure P23.73 Problems 73 and 74.Eight small conducting spheres with identical charge q = 2.00 C are placed at the corners of a cube of side d = 0.500 m (Fig. P23.75). What is the total force on the sphere at the origin (sphere A) due to the other seven spheres? Figure P23.75Two solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare? (a) EA EB = 0 (b) EA EB 0 (c) EA = EB 0 (d) 0 EA EB (e) 0 = EA EB (ii) How do the magnitudes of the electric fields they separately create at radius 4 cm compare? Choose from the same possibilities as in part (i).
- Three small metallic spheres with identical mass m and identical charge +q are suspended by light strings from the same point (Fig. P23.55). The left-hand and right-hand strings have length L and make an angle with the vertical. What is the value of q in terms of k, g, m, L, and ? Figure P23.55A small, charged particle of mass 9.42 x 10-7g and charge +4.50 x 10-12C is sent toward a fixed metal sphere of radius 4.00cm and net charge of 8.50 x 10-8C. (a) If the particle is moving with a speed of 12m/s when it is 32.0cm away from the center of the sphere, does the particle strike the sphere? (b) If so, what is the particle’s speed just before hitting the sphere? (c) If the particle does not strike the sphere, what is its closest distance to the sphere?A small, charged particle of mass 8.60 x 10-7g and charge +4.50 x 10-12C is sent toward a fixed metal sphere of radius 6.00cm and net charge of 6.50 x 10-8C. If the particle is moving with a speed of 12m/s when it is 34.0cm away from the center of the sphere, does the particle strike the sphere? If so, what is the particle’s speed just before hitting the sphere? If the particle does not strike the sphere, what is its closest distance to the sphere?
- An electron, inside an electric field region between two parallel plates as shown below, is projected upward at a speed of v0 = 5.83 x10^6 m/s and at an angle of θ = 39.0°; E = 1870 N/C (directed upward), d = 1.97 cm, and L = 6.20 cm. Will the electron strike one of the two plates? If yes, which plate will it stike and at what distance from the left edge?A dust particle of charge, q, and mass, m, is initially at rest in a uniform electric field with strength of magnitude, E. If the dust particle is then allowed to move freely, how long will it take for the particle to travel a distance, d, in a straight line? (Ignore gravity) a. (md/2qE)1/2 b. (2qEd/m)1/2 c. (qE/2md)1/2 d. (md/qE)1/2 e. (2md/qE)1/2A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = -5.5 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vx = 50 m/s, vy = vz = 0, what is the distance from the origin to the particle at t = 2.0 s? Select one: a. 60 m b. 28 m c. 88 m d. 12 m e. 56 m
