Physics equations/18-Electric charge and field/Q:lineChargesCALCULUS/Quizbank

{A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal B=$$} - &minus;7 - &minus;3 - &minus;3 - 3 + 2 {A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$} - 3&minus;s - 3 - s&minus;7 + 7&minus;s - s&minus;3 {A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where$$\mathcal F=$$} - 2 - 3 + 3/2 - 1/2 {A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:} - 2 - s &minus; 2 - 2 &minus; s -  s &minus; 9 + 9 &minus; s {A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:} - 92 + (7-s)2 - 92 + (2-s)2 - 72 + (2-s)2 - 22 + (7-s)2 + 22 + (9-s)2 {A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:} - 1/2 +  4 -  2 -  8 {A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:} - s&minus;8 - 8&minus;s - s&minus;4 - 4&minus;s + 4 {A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:} - s&minus;8 + 8&minus;s - s&minus;4 - 4&minus;s - 4 {A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:} + 5 -  s&minus;4 - 5&minus;s - 1&minus;s - s&minus;1 {A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:} - 5 -  s&minus;4 - 5&minus;s + 1&minus;s - s&minus;1 {A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:} - 1/2 -  2/3 -  2 +  3/2 -  3 {A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:} - s&minus;3 - 3&minus;s - 8 -  s&minus;7 + 7&minus;s {A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:} - 72 + (8&minus;s)2 - 72 + 82 +  (7-s)2 + 82 - 72 + (3&minus;s)2 - 32 + 82