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2. The electric field is given by the equation E- cy?i+ 2e xyî where c 1000 V/m3. (a) How much work does the electrical field do on a charge of-2 μC taken from point (0,0) along thex axis and then parallel to the y-axis to (1m, 2 m)? (b) How much electrical work is done when the cha moved along a straight line from (0, 0) to (1 m, 2 m)? (c) What is the equation for the electri of this field assuming the origin has a potential of zero? (d) What is the electric potential at point to (1 m, 0) tial (1 m, 2 Solution: Given: q-_2.00 x 10-6 C Drawing c 1000 V/m3 Equations: For path AB: y = 0, dy = 0, and x goes from 0 to 1 m, so WAR-0. For path BC x=lm, dx = 0, and y goes from 0 to 2 m, so wBC-xqcJ2ydy=xqc[y21 8.00x10-3 J For total path WAse Wa+ Wne 8.0 x10" J (0,0) 2m (a) 2m (b) For path AC: y 2x, dy-2 dx, and x goes from 0 to l m, so 4x3 8x311m 38.00x10-3 J (c) V =-JE-dǐ--(fExdx +fEydy)--cU32.dx +fzxydy constant with dx-0 while y goes from 0 to y. For the first part of this path, V-0, and for the second part This must be true along any path, so choose the path y 0, dy- 0, while x goes from 0 to x; then hold x (d) V(l m, 2 m) -4000v

2. The electric field is given by the equation E- cy?i+ 2e xyî where c 1000 V/m3. (a) How much work does the electrical field do on a charge of-2 μC taken from point (0,0) along thex axis and then parallel to the y-axis to (1m, 2 m)? (b) How much electrical work is done when the cha moved along a straight line from (0, 0) to (1 m, 2 m)? (c) What is the equation for the electri of this field assuming the origin has a potential of zero? (d) What is the electric potential at point to (1 m, 0) tial (1 m, 2 Solution: Given: q-_2.00 x 10-6 C Drawing c 1000 V/m3 Equations: For path AB: y = 0, dy = 0, and x goes from 0 to 1 m, so WAR-0. For path BC x=lm, dx = 0, and y goes from 0 to 2 m, so wBC-xqcJ2ydy=xqc[y21 8.00x10-3 J For total path WAse Wa+ Wne 8.0 x10" J (0,0) 2m (a) 2m (b) For path AC: y 2x, dy-2 dx, and x goes from 0 to l m, so 4x3 8x311m 38.00x10-3 J (c) V =-JE-dǐ--(fExdx +fEydy)--cU32.dx +fzxydy constant with dx-0 while y goes from 0 to y. For the first part of this path, V-0, and for the second part This must be true along any path, so choose the path y 0, dy- 0, while x goes from 0 to x; then hold x (d) V(l m, 2 m) -4000v

Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter25: Electric Potential
Section: Chapter Questions
Problem 25.6OQ: In a certain region of space, a uniform electric field is in the x direction. A particle with...
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2. The electric field is given by the equation E- cy?i+ 2e xyî where c 1000 V/m3. (a) How much work does the electrical field do on a charge of-2 μC taken from point (0,0) along thex axis and then parallel to the y-axis to (1m, 2 m)? (b) How much electrical work is done when the cha moved along a straight line from (0, 0) to (1 m, 2 m)? (c) What is the equation for the electri of this field assuming the origin has a potential of zero? (d) What is the electric potential at point to (1 m, 0) tial (1 m, 2 Solution: Given: q-_2.00 x 10-6 C Drawing c 1000 V/m3 Equations: For path AB: y = 0, dy = 0, and x goes from 0 to 1 m, so WAR-0. For path BC x=lm, dx = 0, and y goes from 0 to 2 m, so wBC-xqcJ2ydy=xqc[y21 8.00x10-3 J For total path WAse Wa+ Wne 8.0 x10" J (0,0) 2m (a) 2m (b) For path AC: y 2x, dy-2 dx, and x goes from 0 to l m, so 4x3 8x311m 38.00x10-3 J (c) V =-JE-dǐ--(fExdx +fEydy)--cU32.dx +fzxydy constant with dx-0 while y goes from 0 to y. For the first part of this path, V-0, and for the second part This must be true along any path, so choose the path y 0, dy- 0, while x goes from 0 to x; then hold x (d) V(l m, 2 m) -4000v
Transcribed Image Text:2. The electric field is given by the equation E- cy?i+ 2e xyî where c 1000 V/m3. (a) How much work does the electrical field do on a charge of-2 μC taken from point (0,0) along thex axis and then parallel to the y-axis to (1m, 2 m)? (b) How much electrical work is done when the cha moved along a straight line from (0, 0) to (1 m, 2 m)? (c) What is the equation for the electri of this field assuming the origin has a potential of zero? (d) What is the electric potential at point to (1 m, 0) tial (1 m, 2 Solution: Given: q-_2.00 x 10-6 C Drawing c 1000 V/m3 Equations: For path AB: y = 0, dy = 0, and x goes from 0 to 1 m, so WAR-0. For path BC x=lm, dx = 0, and y goes from 0 to 2 m, so wBC-xqcJ2ydy=xqc[y21 8.00x10-3 J For total path WAse Wa+ Wne 8.0 x10" J (0,0) 2m (a) 2m (b) For path AC: y 2x, dy-2 dx, and x goes from 0 to l m, so 4x3 8x311m 38.00x10-3 J (c) V =-JE-dǐ--(fExdx +fEydy)--cU32.dx +fzxydy constant with dx-0 while y goes from 0 to y. For the first part of this path, V-0, and for the second part This must be true along any path, so choose the path y 0, dy- 0, while x goes from 0 to x; then hold x (d) V(l m, 2 m) -4000v
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