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(a) Find E, and sketch the i, j component of the vector field E in the plane z = 0. (b) Sketch some illustrative field lines (at least 6) for E. (c) Find the field line for E passing through the point (0, 0, 0) (either as a parameterised curve or as an equation). (d) A screen is placed between the two charges, occupying the region {(x, y, z): y = 0). What is the (pointwise) flux through the screen at a point (ro, 0, zo)? (You may take the normal to the screen to point in the direction of increasing y.)

(a) Find E, and sketch the i, j component of the vector field E in the plane z = 0. (b) Sketch some illustrative field lines (at least 6) for E. (c) Find the field line for E passing through the point (0, 0, 0) (either as a parameterised curve or as an equation). (d) A screen is placed between the two charges, occupying the region {(x, y, z): y = 0). What is the (pointwise) flux through the screen at a point (ro, 0, zo)? (You may take the normal to the screen to point in the direction of increasing y.)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Solve (c )and (d )part only in 30 min plz i need perfect soloution plz solve this now
Consider two charged particles, separated by distance d > 0, and located at points (0,2,0) and (0, -2,0) respectively. One has charge q and electric potential 9 41(x, y, z) = V /x² + (y)² + 2² and the other has charge (-q) and electric potential -9 41(x, y, z) = √² + (y + 2)² + 2² Taken as a single system, the electric potential is = 91 +92. The electric field is given by E = -Vy. (a) Find E, and sketch the i, j component of the vector field E in the plane z = 0. (b) Sketch some illustrative field lines (at least 6) for E. (c) Find the field line for E passing through the point (0, 0, 0) (either as a parameterised curve or as an equation). (d) A screen is placed between the two charges, occupying the region {(x, y, z): y = 0}. What is the (pointwise) flux through the screen at a point (zo, 0, zo)? (You may take the normal to the screen to point in the direction of increasing y.) (e) What is the net flux through the portion of the screen {(x, y, z): y=0, x² + z² ≤ 4}? (f) Let C be the closed curve around the edge of the portion of the screen in question (le), with a positive orientation with respect to the normal vector. Find . dr. (g) Let B be a ball of radius R centred at (2R, 2R, 2R), where R >> d (R is much larger than d). Let T be the boundary of the ball. Calculate the net electric flux through the boundary of the ball, E ndS. Hint: you can use an integral theorem here.
Transcribed Image Text:Consider two charged particles, separated by distance d > 0, and located at points (0,2,0) and (0, -2,0) respectively. One has charge q and electric potential 9 41(x, y, z) = V /x² + (y)² + 2² and the other has charge (-q) and electric potential -9 41(x, y, z) = √² + (y + 2)² + 2² Taken as a single system, the electric potential is = 91 +92. The electric field is given by E = -Vy. (a) Find E, and sketch the i, j component of the vector field E in the plane z = 0. (b) Sketch some illustrative field lines (at least 6) for E. (c) Find the field line for E passing through the point (0, 0, 0) (either as a parameterised curve or as an equation). (d) A screen is placed between the two charges, occupying the region {(x, y, z): y = 0}. What is the (pointwise) flux through the screen at a point (zo, 0, zo)? (You may take the normal to the screen to point in the direction of increasing y.) (e) What is the net flux through the portion of the screen {(x, y, z): y=0, x² + z² ≤ 4}? (f) Let C be the closed curve around the edge of the portion of the screen in question (le), with a positive orientation with respect to the normal vector. Find . dr. (g) Let B be a ball of radius R centred at (2R, 2R, 2R), where R >> d (R is much larger than d). Let T be the boundary of the ball. Calculate the net electric flux through the boundary of the ball, E ndS. Hint: you can use an integral theorem here.
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