Name: Lab Day/Time: Wednesday Homework 2 Electric Field Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiplechoice answers must be circled. In the space after the problem, a short justification of each multiple-choice the answer must be included. The open-response answers must be worked out clearly using good physics presentation and will be graded on correctness and how carefully the work is explained. The problems should be worked in the space after the problem on the assignment printout; additional paper may be used if needed. No credit will be given for answers without appropriate supporting work. Minimum good presentation requires the following: (1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3) Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5) Enough English description to allow the reader to have some idea what you are doing without looking at the math. Multiple Choice Problems The questions in this section are to be answered by circling the correct multiple-choice answer AND providing a short justification of your answer in the space after the problem.. Wednesday Homework Problem 2.1 If DNA has a charge of 0.3e per base pair in solution and there are 3 × 109 base pairs in a human genome, then the total charge of the human genome in solution is 1.4 × 10−10 C. If the DNA molecule is placed in an electric field of 100, 000 N C , what would the acceleration of the DNA molecule be? The mass of a DNA molecule is on the order of 3 × 10−15 kg. Select One of the Following: (a) 2 sm2 (b) 3 × 103 sm2 (c) 0.1 sm2 (d) 5 × 109 sm2 (e) 4 × 10−20 sm2 1 Wednesday Homework Problem 2.2 Select the following which best describes the direction of an electric field. Select One of the Following: (a) The electric field points in the direction of higher energy. (b) The electric field points the direction of higher force. (c) The electric field points the direction of the force on a positive charge. (d) The electric field points the direction that any charged object will tend to move if released. Wednesday Homework Problem 2.3 An electric charge with charge q is placed in an electric field with field magnitude E. Due to the field, the charge experiences a force F . If the charge is doubled and the field tripled, how much force is then exerted on the charge? Select One of the Following: (a) F (b) 2F (c) 3F (d) 6F (e) 9F Wednesday Homework Problem 2.4 If the magnitude of the electric field of an infinite plane of charge at a point 10.0m from the plane is |E| = 100.0 N C , what is the surface charge density σ? Select One of the Following: (a) 3.12 × 10−7 C/m2 (b) 1.77 × 10−3 C/m2 (c) 8.85 × 10−10 C/m2 (d) 1.77 × 10−9 C/m2 (e) 0 2 Wednesday Homework Problem 2.5 The figure to the right shows two charged particles with equal but opposite charges ±Q. The two particles are a distance d apart and the negatively charged particle is a distance d from the point a. What is the direction of the electric field at the point a? y -Q a Select One of the Following: (a) The electric field is zero. (b) The electric field points in the positive x direction. (c) The electric field points in the negative x direction. (d) The electric field points in the positive y direction. (e) The electric field points in the negative y direction. 3 +Q x Wednesday Homework Problem 2.6 A positively charged particle with charge +q and a negatively charged particle with charge −2q are placed along the y axis as drawn to the right. The two particles are equidistant from the origin. The drawing is divided into three regions by the dashed lines. Select the region or regions where there is a point with zero electric field (except at infinity). y +q Region 3 Region 2 x -2q Region 1 Select One of the Following: (a) Region 1 only. (b) Region 2 only. (c) Region 3 only. (d) Regions 1 and 3. (e) The electric field is non-zero at all points (except at infinity) in all regions. Wednesday Homework Problem 2.7 Mica is an excellent high voltage insulator. It undergoes dielectric breakdown (sparks) at electric fields of 2.0 × 108 N C . Calculate the force exerted on an electron in mica at this field. Select One of the Following: (a) 5.1 × 10−30 N (b) 1.6 × 10−19 N (c) 3.2 × 10−11 N (d) 2.0 × 108 N (e) 1.2 × 1027 N 4 Wednesday Homework Problem 2.8 Most of you found a linear charge density for the golf tube of around C by modelling the tube as an infinite straight uniform line charge. The golf tube has a radius of −1.0 × 10−7 m about 2.0cm. What is the magnitude of the electric field at the surface of the golf tube if it is modelled as an infinite line of charge? Select One of the Following: (a) 9.0 × 104 N C (b) 4.5 × 104 N C (c) 1.1 × 106 N C (d) 2.2 × 106 N C (e) 6.0 × 103 N C Wednesday Homework Problem 2.9 A point charge q with charge q = 4.0nC is at the point ~r0 = (−4.0cm, 4.0cm, 0). Calculate the electric field at the point ~rP = (−8.0cm, 12.0cm, 0). Select One of the Following: (a) 4495 N C (0.45, −0.89, 0) (b) 4495 N C (0.57, −0.82, 0) (c) 2158 N C (0.57, −0.82, 0) (d) 4495 N C (−0.45, 0.89, 0) (e) 3709 N C (−0.71, 0.71, 0) (f) 2250 N C (−0.45, 0.89, 0) (g) 2250 N C (0.45, 0.89, 0) 5 Wednesday Homework Problem 2.10 In some region of space, the electric field decreases with the distance ~ = (C/x)x̂ where C is a positive constant. Select the drawing below from the origin according to the function, E that best represents this field. (The length of arrows indicates the strength of the electric field at their tail.) Select One of the Following: (a) Figure (a) (b) Figure (b) y x (c) Figure (c) y y y x x x (a) (d) Figure (d) (b) (c) 6 (d) Open Response Questions ~ r) = (50 N , x2 ( N /m2 ), −50 N ). Wednesday Homework Problem 2.11 The electric field in a region of space is given by E(~ C C C (a)Compute the electric field at a point 10m along the positive x-axis. (b)Compute the strength(magnitude) of the electric field at this point. 7 Wednesday Homework Problem 2.12 The electric field near the surface of the earth is 150N/C downward. (a)Compare the electric force on an electron with the gravitational force (size and direction). (b)What charge should be placed on a penny mpenny = .003kg so that the penny would just float near the earth’s surface? 8 Wednesday Homework Problem 2.13 Two infinite line charges have linear charge density 3.0µC/m. One line charge runs parallel to the y axis. The other line charge is parallel to the z axis. The charges are located as drawn. The distance d = 4.0cm. line charge 2 line charge 1 (a)Calculate the electric field at point P (report as vector). d (b)Draw the electric field vectors at point P and the resultant electric field vector. P (c)Draw the direction of the force that the field would exert on a negative charge placed at point P . d/2 y d 9 x Wednesday Homework Problem 2.14 A charged golf tube (modelled as an infinite line charge), charged board (modelled as an infinite plane charge), and charged pith ball (modelled as a point charge) are placed as shown to the right. The plane charge has charge density 0.26µC/m2 and is located in the x − y plane. The golf tube is negatively charged with linear charge density −0.030µC/m and runs parallel to the y-axis through the point (−10.0cm, 0, 10.0cm). The pith ball has charge +10.0nC and is located at (10.0cm, 0, 10.0cm). We will compute the electric field at a point P at 5.0cmẑ. (a)Draw the direction of the electric field of each object at point P . ~ pith,P , at point P , from the (b)Compute the electric field, E pith ball. ~ line,P , at point P , from the (c)Compute the electric field, E golf tube. ~ board,P , at point P , from (d)Compute the electric field, E the charged board. (e)Compute the total electric field at point P . 10 z λ<0 Q pith golf tube P charged board x