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

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A
A line charge 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: $$\frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where: { $$\mathcal A=$${ -3 }
 * type="{}"}

{ $$\mathcal B=$${ 2 }
 * type="{}"}

{ $$\mathcal C=$${ 7-s }
 * type="{}"}

{ $$\mathcal D=$${ 3 }
 * type="{}"}

{ $$\mathcal E=$${ 7-s }
 * type="{}"}

{ $$\mathcal F=$${ 3/2 }
 * type="{}"}

B
A line charge 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: $$\frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where: { $$\mathcal A=$${ 2 }
 * type="{}"}

{ $$\mathcal B=$${ 7 }
 * type="{}"}

{ $$\mathcal C=$${ 9-s }
 * type="{}"}

{ $$\mathcal D=$${ 2 }
 * type="{}"}

{ $$\mathcal E=$${ 9-s }
 * type="{}"}

{ $$\mathcal F=$${ 3/2 }
 * type="{}"}

C
A line charge 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: $$\frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where: { $$\mathcal A=$${ 4 }
 * type="{}"}

{ $$\mathcal B=$${ 8 }
 * type="{}"}

{ $$\mathcal C=$${ 4 }
 * type="{}"}

{ $$\mathcal D=$${ 8-s }
 * type="{}"}

{ $$\mathcal E=$${ 4 }
 * type="{}"}

{ $$\mathcal F=$${ 3/2 }
 * type="{}"}

D
A line charge 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: $$\frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where: { $$\mathcal A=$${ 4 }
 * type="{}"}

{ $$\mathcal B=$${ 6 }
 * type="{}"}

{ $$\mathcal C=$${ 1-s }
 * type="{}"}

{ $$\mathcal D=$${ 5 }
 * type="{}"}

{ $$\mathcal E=$${ 1-s }
 * type="{}"}

{ $$\mathcal F=$${ 3/2 }
 * type="{}"}

E
A line charge 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: $$\frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where: { $$\mathcal A=$${ 3 }
 * type="{}"}

{ $$\mathcal B=$${ 7 }
 * type="{}"}

{ $$\mathcal C=$${ 7-s }
 * type="{}"}

{ $$\mathcal D=$${ 7-s }
 * type="{}"}

{ $$\mathcal E=$${ 8 }
 * type="{}"}

{ $$\mathcal F=$${ 3/2 }
 * type="{}"}