1308 E&M Reviews for the final exam Charge conservation: The Sun generates most of its light through a series of nuclear reactions called the proton-proton chain. The overall process of these nuclear reactions can be summarized as 4 1H → 2He + 2ν + 2γ + 2? where ν is a small neutral particle called a neutrino, and γ is a photon (a particle of light), which is also neutral. The pre-subscripts on the element symbols H (hydrogen) and He (helium) indicate the number of protons in the nucleus of each element. What is the charge of the unknown entity "?" ? Charge induction: You are locked in a rubber room and given a pair of rubber gloves along with a positively charged bar of gold (marked with a "+") and two electrically neutral bars of gold. You will be released if you can produce a negatively charged bar of gold, and you get to keep the gold. Explain how you might accomplish this 1308 E&M Coulomb’s Law of electrostatic forces Coulomb’s Law + friction concept: Two 2.0 kg plastic garbage cans are sitting 2.6 meters apart on a sticky classroom floor (coefficient of static friction μs = 0.40). They are not moving. If the first one has a charge of 10 μC, find (a) the most negative possible charge and (b) the most positive possible charge for the other garbage can. Assume that the charges can be represented as point charges located at the cans' centers. Use the concept of symmetry: A bicycle wheel with radius 35 cm has 73 charges (1.0 μC each) spaced at regular intervals along its edge. A flea with charge −0.010 μC lands in the center of the wheel. (a) What is the net electric force on the flea? (b) One of the charges is removed. Find the magnitude of the new net electric force on the flea. 1308 E&M Coulomb’s Law of electrostatic forces Coulomb’s law + other physics concepts: Two 0.600 kg oppositely charged basketballs are following a clockwise circular path on a frictionless, freshly waxed basketball court. The balls are on opposite sides of the circle at all times, and are 10.0 m apart. Their charges cause the balls to continue on the circular path at a speed of 1.20 m/s. (a) Determine the product of the charges on the basketballs. (b) Now assume the charge on the positively charged ball is twice the magnitude of the negatively charged one. Determine the charge on the negative ball. (c) Determine the charge on the positive ball. (d) The same basketballs are now 5.00 m apart, but they are still moving in a circular path. Determine their speed. (e) One of the basketballs now has a mass of only 0.550 kg. Is it still possible for the two balls to hold each other so that they travel along identical circular paths? Explain your answer. 1308 E&M Electric field 1. Three locations, 1, 2, and 3, are labeled in the electric field diagram. At which of these locations is the strength of the field the greatest? 2. In the diagram, two charges of +2q and −5q are placed on a line. (a) There is a point on the line where the strength of the electric field due to the two charges is zero. Describe where the point is, relative to the positions of the two charges. (b) Is there any point not on the line, where the strength of the electric field is zero? 1308 E&M Electric field and Gauss’s law 1. A solid conducting sphere with a radius of 35.4 cm contains a total charge of 5.46 mC, evenly distributed over its surface. (a) What is the direction of the electric field at its surface? (b) What is the strength of the electric field at its surface? 1308 E&M Electric potential 1. The gravitational potential energy of all the water stored behind a very large dam is 1.2×1016 J, using the base of the dam as the reference point for zero PE. Imagine you could store the same amount of potential energy in a system consisting of two particles, each with a charge of 0.0020 C. How far apart should you place the charges? (3.0e−12 m) 2. Two infinitesimally small point charges of +2.0 μC each are initially stationary and 5.0 m apart. (a) How much work is required to bring them to a stationary position 2.0 m apart? (b) 2.0 mm apart? (c) With a finite amount of energy, is it possible to push them together? 3. A charge of +3.00 μC is placed at the point (0 m, 0 m, 0 m); a charge of −4.50 μC is placed at the point (2.00 m, −5.00 m, 7.00 m); finally, a charge of −1.00 μC is placed at the point (1.00 m, 1.00 m, 1.00 m). (a) What is the electric potential energy of this configuration? (b) If a neutron (a particle with the mass of the proton but no electric charge) is brought in from infinity and placed at the point (−3.00 m, 2.00 m, 5.50 m), how does the electric potential energy of the configuration change? ((a) −2.46e−2 J (b) It stays the same ) 1308 E&M Electric potential 1. A certain 4.8-volt cellular telephone battery has a capacity of 600 mAh. (One mAh equals 3.6 coulombs.) When the battery's charge is too low to run the phone any longer (assume it is zero), the battery must be recharged. (a) How much work is done by the recharger? (b) If electricity costs you 9.0 cents per kWh, how much does one recharge cost you? ((a) 1.04e4 J (b) $ 2.6e−4 ) 2. In the diagram you see the spark gap between the contacts of an automobile spark plug. When the contacts are charged to a potential difference great enough to cause a spark to jump across the gap, the electric field between them approximates a uniform field of strength 3.1×106 N/C. What is the magnitude of the potential difference that causes the spark? (710 V) 1308 E&M Gauss’s Law 1. A cube with 1 m edges is in a uniform electric field of magnitude 17 N/C. The electric field intersects the top of the cube at a 30° angle to the normal, and is parallel to two faces of the cube. The area vector for each face of the cube points outward. (a) What is the relationship between the electric flux through the top face and the electric flux through the bottom face? (b) Calculate the net electric flux through the entire surface of the cube. ((a) They have equal magnitude but opposite signs (b) 0 (N/C)·m2) 2. A vertical, infinite, nonconducting plane has uniform positive charge. A weightless thread is attached to the plane, and at the end of the thread there is a small spherical ball with a charge of +78.6 μC, and a mass of 0.954 kg. The angle that the thread makes with the plane is 37.3°. What is the charge density σ of the plane? 1308 E&M Gauss’s Law 1. Consider a rectangular slab, infinite in length and width and extending a distance h/2 on either side of the yz plane, so that it has a finite thickness h. The slab has a constant positive charge density ρ. (a) In what direction does the electric field point for positive x? (b) In what direction does the electric field point for negative x? (c) Determine the electric field inside the slab, for 0 < x < h/2, using Gauss' Law. (d) Determine the electric field outside the slab, for x > h/2, using Gauss' Law. ((a) In the positive x direction. (b) In the negative x direction. (c) ρx/ε0 (d) ρh/2ε0 ) 1308 E&M Direct current, resistance 1. Two like charges of one coulomb each, separated by one meter, repel each other with a force of 8.99×109 N, equivalent to the weight of 10 battleships. A flashlight bulb may have a current of 0.40 A flowing through it, which is equivalent to one coulomb of charge flowing through every 2.5 seconds. But a flashlight circuit is clearly not subject to tremendous electrostatic forces – or even small ones. Why not? 2. Two wires are connected to a conducting sphere of radius 7.75 cm, which is initially uncharged. One wire carries a current of 3.47 μA into the sphere, and another wire carries a current of 1.26 μA out of the sphere. How long does it take to to produce an electric potential of 5.00 MV at a distance of 11.6 cm away from the center of the sphere? 3. The graphite in a pencil has a resistivity of 7.84×10−6 Ωm. The graphite's diameter is 0.700 mm and its length is 40.0 mm. (a) Find the resistance of this graphite "wire." (b) Find the diameter of a cylindrical copper wire of the same length (having resistivity 1.70×10−8 Ωm) that would produce the same resistance.
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