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- A Van de Graaff generator is one of the original particle accelerators and can be used to accelerate charged particles like protons or electrons. You may have seen it used to make human hair stand on end or produce large sparks. One application of the Van de Graaff generator is to create X-rays by bombarding a hard metal target with the beam. Consider a beam of protons at 1.00 keV and a current of 5.00 mA produced by the generator, (a) What is the speed of the protons? (b) How many protons are produced each second?A Van de Graaff generator (see Fig. 25.23) is operating so that the potential difference between the high-potential electrode and the charging needles at is 15.0 kV. Calculate the power required to drive the belt against electrical forces at an instant when the effective current delivered to the high-potential electrode is 500 A. Figure 25.23 Schematic diagram of a Van de Graaff generator. Charge is transferred to the metal dome at the top by means of a moving belt.An all-electric car (not a hybrid) is designed to run from a bank of 12.0-V batteries with total energy storage of age of 2.00 107J. If the electric motor draws 8.00 kW as the car moves at a steady speed of 20.0 m/s. (a) what is the current delivered to the motor? (b) How far can the car travel before it is out of juice"?
- You are working with an oceanographer who is studying how the ion concentration in seawater depends on depth. She shows you the device that she uses to measure the resistivity of water from a boat. It consists of a pair of concentric metallic cylinders at the end of a cable (Fig. P26.36). Seawater flows freely between the two cylindrical shells. She makes a measurement by lowering the device into the water and applying a potential difference V between the inner and outer cylinders. This produces an outward radial current I in the seawater between the shells. She shows you the current and voltage data for the water at a particular depth and is then called away to answer a long call on her cellphone about a laboratory issue back on the mainland. As she leaves, she says, Have the resistivity of the water calculated when I get back. She forgot to show you any tables or formulas to use to determine the resistivity, so you are on your own. Quick! Find an expression for the resistivity in terms of I and V before she finishes her phone call! Figure P26.36The immediate cause of many deaths is ventricular fibrillation, an uncoordinated quivering of the heart, as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes start organized beating again. A defibrillator is a device that applies a strong electric shock to the chest over a time of a few milliseconds. The device contains a capacitor of a few microfarads, charged to several thousand volts. Electrodes called paddles, about 8 cm across and coated with conducting paste, are held against the chest on both sides of the heart. Their handles are insulated to prevent injury to the operator, who calls Clear! and pushes a button on one paddle to discharge the capacitor through the patient's chest Assume an energy of 3.00 102 W s is to be delivered from a 30.0-F capacitor. To what potential difference must it be charged?Consider a square rod of material with sides of length L = 3.00 cm with a current density of J=J0eaxk=(0.35Am2)e(2.1103m1)xk as shown below. Find the current that passes through the face of the rod.
- The batteries of a submerged non-nuclear submarine supply 1000 A at full speed ahead. How long does it take to move Avogadro’s number (6.02 1023) of electrons at this rate?A 12-V car battery is used to power a 20.00-W, 12.00-V lamp during the physics club camping trip/star party. The cable to the lamp is 2.00 meters long, 14-gauge copper wire with a charge density of n=9.501028m3 . (a) What is the current draw by the lamp? (b) How long would it take an electron to get from the battery to the lamp?A particle accelerator produces a beam with a radius of 1.25 mm with a current of 2.00 mA. Each proton has a kinetic energy of 10.00 MeV. (a) What is the velocity of the protons? (b) What is the number (n) of protons per unit volume? (b) How many electrons pass a cross sectional area each second?
- An x-ray tube used for cancer therapy operates at 4.0 MV, with a beam current of 25 mA striking the metal target. Nearly all the power in the beam is transferred to a stream of water flowing through holes drilled in the target. What rate of flow, in kilograms per second, is needed if the rise in temperature (T) of the water is not to exceed 50.C?In a Geiger counter, a thin metallic wire at the center of a metallic tube is kept at a high voltage with respect to the metal tube. Ionizing radiation entering the tube knocks elections off gas molecules or sides of the tube that then accelerate towards the center wire, knocking off even more electrons. This process eventually leads to an avalanche that is detectable as a current. A particular Geiger counter has a tube of radius K and the inner wire of radius a is at a potential of V0 volts with respect to the outer metal tube. Consider a point P at a distance s from tine center wire and far away from the ends, (a) Find a formula for the electric field at a point P inside using tine infinite wire approximation, (b) Find a formula for the electric potential at a point P inside. (c) Use V0 = 900 V, a = 3.00 min. P = 2.00 cm, and find the value of the electric field at a point 1.00 cm from the center.Check Your Understanding Copper wires use routinely used for extension cords and house wiring for several reasons. Copper has the highest electrical conductivity rating, and therefore the lowest resistivity rating, of all nonprecious metals. Also important is the tensile strength, where the tensile strength is a measure of the force required to pull an object to the point where it breaks. The tensile strength of a material is the maximumamount of tensile stress it can take before breaking. Copper has a high tensile strength, 2108Nm2 A thirdimportant characteristic is ductility. Ductility is a measure of a material’s ability to be drawn into wires and a measure of the flexibility of the material, and copper has a high ductility. Summarizing, for a conductor to be a suitable candidate for making wire, there are at least three important characteristics: low resistivity, high tensile strength, and high ductility. What other materials are used for wiring and what are the advantages and disadvantages?