Exam 19: The First Law of Thermodynamics

Spheres of charge: A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The excess charge on this sphere is closest to

Potential due to point-charges: A -7.0-μC point charge has a positively charged object in an elliptical orbit around it. If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges, what is the maximum electric potential difference through which the positive object moves? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Electric field and potential: A negative charge, if free, will tend to move

Potential energy of point-charges: Two equal positive charges are held in place at a fixed distance. If you put a third positive charge midway between these two charges, its electrical potential energy of the system (relative to infinity) is zero because the electrical forces on the third charge due to the two fixed charges just balance each other.

Potential due to point-charges: Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively. Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Spheres of charge: A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity?

Potential due to point-charges: A half-ring (semicircle) of uniformly distributed charge Q has radius R. What is the electric potential at its center?

Electric field and potential: In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y) = 2xy - x² - y, where x and y are measured in meters and V is in volts. At which point is the electric field equal to zero?

Electric field and potential : Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)

Potential energy of point-charges: A tiny object carrying a charge of + 3.00 μC and a second tiny charged object are initially very far apart. If it takes of work to bring them to a final configuration in which the object i is at x = 1.00 mm, y = 1.00 mm, and the other charged object is at x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge on the second object. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Charged ring: A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius. A point charge q = +530 nC is fixed at the center of the ring. Points A and B are located on the axis of the ring, as shown in the figure. What is the minimum work that an external force must do to transport an electron from B to A? (e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Potential due to point-charges: Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) (a) What is the potential at point A (relative to infinity) due to these charges? (b) What is the potential at point B (relative to infinity) due to these charges?

Potential energy of point-charges: A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart. How much work does it take to bring the -3.0-μC charge to x = 3.0 mm, y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm, y = 0.00 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Potential energy of point-charges: An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 0.0030c, where c is the speed of light. What is their distance of closest approach? Hint: There are two conserved quantities. Make use of both of them. (c = 3.00 × 10⁸ m/s, k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C, mproton = 1.67 × 10^-27 kg)

Electric field and potential: If the electric potential in a region is given by V(x) = 6/x², the x component of the electric field in that region is