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Problem 17B (Electric Force Vectors)
1. The SydneyHarbourBridge, in Australia, is the world’s widest long-spanbridge. Suppose two charges, −12.0 nC and −68.0 nC, are separated bythe width of the bridge. The electric potential along a line between thecharges at a distance of 16.0 m from the −12.0 nC charge is −25.3 V. Howfar apart are the charges?
ADDITIONAL PRACTICE
2. The Hughes H4 Hercules, nicknamed the Spruce Goose, has a wingspanof 97.5 m, which is greater than the wingspan of any other plane. Supposetwo charges, 18.0 nC and 92.0 nC, are placed at the tips of thewings. If an electric potential of 53.3 V is measured at a certain pointalong the wings, how far is that point from the 92.0 nC charge?
3. A Canadian company has developed a scanning device that can detectdrugs, explosives, and even cash that are being smuggled across stateborders. The scanner uses accelerated protons to generate gamma rays,which can easily penetrate through most substances that are less than afew centimeters thick. At the heart of the scanner is a compact powersupply that can produce an electric potential as large as 1.0 x 10^6 V. Findthe value of a point charge q that would create an electric potential of1.0 x 10^6 V at a distance of 12 cm.
4. Gravitational potential and electric potential are described by similarmathematical equations. Suppose Earth has a uniform distribution of positivecharge on its surface. A test particle with a mass of 1.0 kg and a chargeof 1.0 C is placed at some distance from Earth.What must the total chargeon Earth’s surface be for the test particle to experience equal gravitationaland electric potentials? (Hint: Obtain the equation for gravitational potentialby comparing the gravitational force equation from Section 7I toCoulomb’s law for electrostatic force.Assume that the entire charge onEarth’s surface can be treated as a point charge at Earth’s center.)
5. Overall, the matter in the sun is electrically neutral. However, the temperatureswithin the sun are too high for electrons to remain with positivelycharged nuclei for more than a fraction of a second. Suppose thepositive and negative charges in the sun could be separated into twoclouds with a separation of 1.5 x 10^8 km, which is equal to the averagedistance between Earth and the sun.
a. Calculate the charge in each cloud. Assume that the sun, which hasa mass of 1.97 x 10^30 kg, consists entirely of hydrogen. The mass ofone hydrogen atom is 1.67 x 10^−27 kg.
b. Calculate the electric potential for the two clouds at a distance of1.1 x 10^8 km (the distance between the sun and Venus) from theproton cloud.
6. The freight station at Hong Kong’s waterfront is the largest multilevel industrialbuilding in the world. The station is 292 m long and 276 m wide,and inside there are more than 26 km of roadways. Consider a rectanglethat is 292 m long and 276 m wide. If charges +1.0q, −3.0q, +2.5q, and+4.0q are placed at the vertices of this rectangle, what is the electricpotential at the rectangle’s center? The value of q is 64 nC.
7. The largest premechanical earthwork was built about 700 years ago inAfrica along the boundaries of the Benin Empire. The total length of theearthwork is estimated to be 16 000 km. Consider an equilateral trianglein space formed by three equally charged asteroids with charges of7.2 x 10^−2 C. If the length of each side of the triangle is 1.6 x 10^4 km,what is the electric potential at the midpoint of any one of the sides?
8. The Royal Dragon restaurant in Bangkok, Thailand, can seat over 5000customers, making it the largest restaurant in the world. The area of therestaurant is equal to that of a square with sides measuring 184 m each. Ifthree charges, each equal to 25.0 nC, are placed at three vertices of thissquare, what is the electric potential at the fourth vertex?