Exam #2, Electrostatics Prof. Maurik Holtrop Department of Physics PHYS 408 University of New Hampshire March 27 th, 2003 Name: Stuent # NOTE: There are 5 questions. You have until 9 pm to finish. You must staple your Formula-sheet to the back of this exam when haning it in. You are allowe to use your calculator. Work out all problems using variables, then put in numbers. Partial creit can only be given to clearly worke out problems. Useful information: 1 9 2 k = 8.99 10 Nm C 4πε = 0-2 ε 0 = 8.85 10 C N m 12 2-1 -2 e = 19 1.60 10 C 8 19 6 Spee of light: c = 3x10 m/s 1 ev = 1.60 10 J 1 MeV = 10 ev Mass of an electron: M e = 0.5 MeV/c 2 Mass of a proton (approx.): M p =1000MeV/c 2 Problem Description Available Points Score I Electron at origin 20 II Dipole in E fiel 20 III Parallel metal plates 20 IV Spherical Shells 20 V Charge semi circle 20 Page 1 of 7
I) Note: In this problem express all your answers in terms of the relevant variables, i.e. use e, r, an constants. A single electron is place at the origin. a) What is the equation for the electric vector fiel ue to this electron at a istance r from the origin? b) What is the equation for the electric potential ue to this electron at a istance r from the origin? c) A secon electron is now brought from infinity an place on the x axis at x=. What is the force (magnitue an irection) on this secon electron ue to the first? ) (See part c.) What is the amount of work that nees to be one to place this secon electron? Page 2 of 7
E E E +q -q -q +q -q +q A B C II) An electric ipole consisting of 2 charges of magnitue 2 nc, separate by 5µm, is place in a uniform electric fiel of strength 150 N/C. We o this 3 times, in 3 ifferent orientations, A, B, an C. a) What is the ipole moment p for this ipole? Inicate in the picture what irection the vector points relative to the + an charge. b) What is the net force (magnitue an irection) on the ipole for each of the 3 orientations? c) What is the net torque (magnitue an irection) on the ipole for each of the 3 orientations? ) What is the potential energy, U, for each of the 3 orientations? Page 3 of 7
V= +500V V= -500V III) Two infinite metal plates in the z-y plane are separate by a istance,, of 5 cm. The left plate is hel at a potential of V left = +500V an locate at x=-2.5cm, the right plate is locate at x= +2.5cm an hel at a potential of V right = -500V. a) Draw the electric fiel lines, inicating the irection of the fiel with arrows. Also raw the equipotential surfaces as ashe lines. b) If a proton is release right at the surface of the left plate, what is the velocity of this proton when it hits the right plate? (express your answer in terms of the spee of light, c, ignore gravity) c) What woul be the equation for the potential anywhere between the plates? (Hint: this means, V(x) = some function of x) Page 4 of 7
) Using the result from c, what is the electric fiel anywhere between the plates? e) What is the surface charge ensity on each of the plates? (Hint: Use the result you get for the electric fiel from Gauss law an from part ) Page 5 of 7
Q C B A R 1 R 2 IV) The iagram shows a thick metal sphere, with a thickness an inner raius R 2, insie of which is a smaller thin metal sphere with raius R 1. The inner sphere has a charge of Q place on it, the outer sphere is overall neutral. a) What is the magnitue an irection of the electric fiel in region A, with r< R 1? b) What is the magnitue an irection of the electric fiel in region B, where R 1 <r<r 2? c) What is the magnitue an irection of the electric fiel in region C, insie the outer metal shell, where R 2 <r< (R 2 +)? ) What is the inuce surface charge ensity σ 2 on the inner surface of the thick shell? (The charge ensity that sits on the surface at r=r 2 ) e) If your answer for ) is given as σ 2 (which coul be either positive or negative), what is the charge ensity, σ 3, on the outer surface of the thick shell? (r=r 2 +) Page 6 of 7
q R θ y C x V) A section of a thin plastic circle with raius R spans an arc of π raians. It has a charge Q uniformly istribute on it. For the point C in the center of this circle: A) Draw the vector for the contribution to the E fiel of the small charge element q in the picture, label this E q, also raw the vector E fiel ue to the total charge Q, label this E tot. B) Setup the equation for the contribution to the E fiel at point C ue to the small charge element q on the circle. C) Setup the integral for the E fiel at point C, incluing the limits. D) Calculate the electric fiel at point C. Express your answer in terms of Q an R. Page 7 of 7