Module 1 Problem 7 and 8

(109%) Problem 7: A 3-D printer lays down a semicircular arc of positively charged plastic with a radius R = 2.6 cm, and a linear charge density of 1 = +1.7 C/m. After the printer has finished the arc, the stylus moves to the center of the are as shown. The minute segment of the plastic arc highlighted in the diagram subtends an angle de. Note the measurement of the angle @ shown in the figure.\f& 14% Part (a) Input a symbolic expression for the charge do on the segment of charge of size de in terms of given parameters. Grade Summary dq = Deductions 046 Potential 1009% cos(8) sin(8) 7 HOME Submissions Attempts remaining 10 1 4 6 (596 per attempt) de dr e 1 2 3 detailed view m -+ 0 END ge R t VO BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 09% deduction per hint. Hints remaining: 3 Feedback: 096 deduction per feedback.14% Part (b) Input a symbolic expression for the electric force vector, exerted by the minute segment of plastic subtending the arc de on an electron (charge - @). within the stylus at the center of the arc. Express your answer in terms of given parameters, fundamental constants, and the unit vectors i and j in the specified coordinate system. Grade Summary dF = Deductions 096 Potential 1009% 7 HOME Submissions Attempts remaining: 10 4 5 6 (596 per attempt) 1 2 detailed view -+ 0 END VO BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 09% deduction per hint. Hints remaining: 1 Feedback: 09% deduction per feedback.&14% Part (c) Find the indefinite integral of the x-component , from part (b), but do not evaluate the limits. Grade Summary F. Deductions 096 Potential 1009% cos(8) zin (0) 7 HOME Submissions Attempts remaining 10 de 6 (596 per attempt) dr e g 2 3 detailed view m 0 END qe R t BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 09% deduction per hint. Hints remaining: 2 Feedback: 096 deduction per feedback.14% Part (d) Select the limits of integration that would result in the correct calculation of the force exerted by the entire line of plastic on an electron in the stylus as shown in the diagram. Or = 0 to r = R Grade Summary Deductions 096 08= x to 8=0 Potential 10096 O 8 = 0 to 8 = x Submissions Or = 0 to = 0 Attempts remaining 4 0 8=-7/2 to 8 = 1/2 (2596 per attempt) detailed view Submit Hint Feedback I give up! Hints: 096 deduction per hint. Hints remaining: 3 Feedback: 09% deduction per feedback.14% Part (e) Using the limits from part (d) and the expression from part (c) to determine an expression for the magnitude of the electrical force exerted by the positively charged line of plastic on the electron in the stylus. F = Grade Summary Deductions 096 Potential 1009% cos(8) zin(0) B 7 HOME Submissions e 4 Attempts remaining 10 (596 per attempt) de dr e 1 3 detailed view h k + END ge R BACKSPACE INII. CLEAR Submit Hint Feedback I give up!14% Part (f) Calculate the magnitude of the electric force, in newtons, exerted by the positively charged line of plastic on the electron in the stylus. Grade Summary F = Deductions 096 Potential 100 96 si( ) cos() tan() 7 9 HOME Submissions Attempts remaining 10 cotan( ) acoso E 5 (596 per attempt) atan() acotan() sinh() 1 2 3 detailed view cosh() tanh() cotanh() END O Degrees O Radians BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 09% deduction per hint. Hints remaining: 2 Feedback: 096 deduction per feedback.14% Part (g) What direction is the electric force exerted on the electron in the stylus? Grade Summary O Out of the page Deductions OInto the page Potential 1009% O Up Submissions O Cannot be determined with the information given Attempts remaining: 7 (149% per attempt) OLeft detailed view O Down O Some other direction not offered ORight Submit Hint Feedback I give up! Hints: 0 for a 096 deduction. Hints remaining: _0 Feedback: 09% deduction per feedback.(10%) Problem 8: A plastic rod of length d= 1.5 m lies along the x-axis with its midpoint at the origin. The rod carries a uniform linear charge density 1 = 2.5 nC/m. The point P is located on the postive y-axis at a distance yo = 15 cm from the origin. The z-axis points out of the screen.\f&25% Part (a) By symmetry the electric field at point P has no component in the Grade Summary Oz direction Ox direction Deductions 046 Oy and z directions Ox and z directions Potential 10040 Ox and y directions Oy direction Submissions Attempts remaining: 5 (2096 per attempt) detailed view Submit Hint Feedback I give up! Hints: 096 deduction per hint. Hints remaining: 3 Feedback: 096 deduction per feedback.25% Part (b) Choose the correct expression for the y-component of the electric field at P due to a thin slice of the rod of thickness ch located at point x. Grade Summary O O Deductions 046 krx Potential 10096 dE. = de dEy = (x2 + 1/3)3/2 de dEy = (x2 + y/7)3/2d Submissions Attempts remaining: 5 O O O (2096 per attempt) kyoA A KA detailed view dE, = (x2 + 17)3/20 dBy = dE, = (x2 + Vo) (x2 + yo) Submit Hint Feedback I give up! Hints: 096 deduction per hint. Hints remaining: 4 Feedback: 096 deduction per feedback.25% Part (c) Integrate your correct choice in part (b) over the length of the rod and choose the correct expression for the y-component of the electric field at point P. O O Grade Summary O Deductions 096 2kd 2kAd 2kAd Potential 10046 Ey = Ey Ey = yo vd2 + yo youd' + 4y's yo v d' + yo Submissions O Attempts remaining: 3 (339% per attempt) 2Ad detailed view Ey = yo v d2 + yo Submit Hint Feedback I give up! Hints: 096 deduction per hint. Hints remaining: 2 Feedback: 09% deduction per feedback.& 25% Part (d) Calculate the magnitude of the electric field at point P, in newtons per coulomb. Grade Summary E = Deductions 046 Potential 10090 sing tan() 7 9 HOME Submissions Attempts remaining: 10 cotan() asin() acos( 4 6 (596 per attempt) atan() acotan() sinhO 1 2 3 detailed view coshO tanh() cotanh() END O Degrees O Radians BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 096 deduction per hint. Hints remaining: 2 Feedback: 09% deduction per feedback