Problems 1. Electric force and field (7 points) Two point charges, Q1 = 5.4 x 10-7 C and O2 = 2.6 x 10- C, are located L = 4.3 m apart, as shown in the figure below. Point P is d, = 3.9 m to the right of Q, and d2 = 1.8 m below Q2. The angle 0 = 24.8. (a) (3 points) What is the electric force on Q, due to Q2? Give both the magnitude and direction of the force. Is the force attractive or repulsive? (b) (4 points) What is the electric field at point P? Give the x and y components of the electric field. J ( 3. 9 ) 2 + ( 1,8 ) O2 4.3 L d2 1. Sch X P2. Four charges (7 points) Four charges O, = 7C, 0, =4C, 0; = 4C, and : Q4 = 6 C are shown in the figure below, along with the electric field lines sourced by these charges. However, the arrows on the field lines are missing. In addition, three 'lc.o.ca, B, and C are shown, and a spherical Gaussian surface is indicated by a dottqd( _[I:ne (a) (2 points) For each electric field line in the figure, add an arrow indicating (You can write the arrows directly on the exam sheet, or you can copy the fig blue exam book.) (b) (1 point) What is the direction of the force on a positive charge located a (c) (1 point) What is the direction of the force on a negative charge located a (d) (1 point) Is the voltage higher at point A, is it higher at point C, or are the and C equal? (e) (2 points) What is the electric flux through the Gaussian surface? neutrons, toward a large, flat, uniformly positively charged w\\ as shown in the figure below. Just after being thrown, the r 275eV. The charged wall generates a uniform ele (@) (2 points) What Is the voltage difference between the wall and location at which Prof. Lippert throws the nucleus? (b) (3 points) Does the nucleus reach the wall? If so, what is its kinetic energy when it hits the wall? If not, how close to the wall does it get, and when happens to the nucleus instead? 4. Ball and shell (6 points) A conducting metal ball of radius R, = 0.11 m and charge q; = 3.9 x 1077 C is located at the center of a thin, hollow, non-conducting shell of radius R, = 0.87 m and charge , = 8.3 x 10~? C uniformly distributed over it, as shown in the figure below. (a) (1 point) How many more electrons than protons are in the metal ball? (b) (3 points) Draw the electric field lines in each of the three regions: (1) Inside the metal ball, (2) between the ball and shell, and (3) outside the shell. If the electric field is zero in any of these regions, write = () instead of drawing field lines. (Copy the figure into your blue exam book and draw the electric field lines there.) (c) (2 points) What is the voltage difference befween the metal ball and the thin shell? 5. Rod (extra credit - 4 points) A thin, nonconducting rod of length L = 2 m carries a s uniform charge per unit length A = 1.8 X 1078 C/m, as shown in the figure below. hat the electric potential at point P, a distance d = 3 m from the end of the rod? Hint: y i du want to use the integral: | = Inwu u