We would like to calculate the magnitude of the electric potential at a point Pa distance a to right of a square composed of charged rods. 1- +1 + + + + + + Each rod has total charge Q and is length l. The point P is à distance a to right of the mid- point of the right rod. The width of the rods is negligible compared to all other distances in the problem. Which of the following is the correct integral expression for the potential? Hint: set the origin of your coordinates at the center of the square and label the horizon- tal coordinate x' in the integral.

Physics for Scientists and Engineers: Foundations and Connections
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Chapter26: Electric Potential
Section: Chapter Questions
Problem 67PQ: A charged particle is moved in a uniform electric field between two points, A and B, as depicted in...
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We would like to calculate the magnitude of
the electric potential at a point Pa distance a
to right of a square composed of charged rods.
+ +++ + + +
Each rod has total charge Q and is length I.
The point P is à distance a to right of the mid-
point of the right rod. The width of the rods
is negligible compared to all other distances
in the problem. Which of the following is the
correct integral expression for the potential?
Hint: set the origin of your coordinates at
the center of the square and label the horizon-
tal coordinate x' in the integral.
Transcribed Image Text:We would like to calculate the magnitude of the electric potential at a point Pa distance a to right of a square composed of charged rods. + +++ + + + Each rod has total charge Q and is length I. The point P is à distance a to right of the mid- point of the right rod. The width of the rods is negligible compared to all other distances in the problem. Which of the following is the correct integral expression for the potential? Hint: set the origin of your coordinates at the center of the square and label the horizon- tal coordinate x' in the integral.
Q (+')² + (1/2)²)3/2|
1/2
4TEol
1.
(r+1)2+y
I dz
(r+)2+(1/2)²
-1/2
1/2
4meol
-1/2
H/2
dy
-1/2
Q
2.
1
2Teol
V(I+1)? + y²
Q
dy
-1/2
(1² + y²)3/2' ((I + 1)2 + y²)3/2
3.
1/2
r' da
4Teol
-1/2
/2 (+)2+(!/2)²)3/2
N/2
dy
Q
4TEOl
4.
+.
(x2 + y²)3/2 ((x+1)2 + y²)3/2
(+x')dr'
1/2 ((x+')2+(!/2)²)3/2
4TEol
N/2
dy
(x² + y?)3/2
1
1
4TEOl
5.
((r +1)2 + y²)3/2
1/2
dr
4neol
1/2
((* +x')² + (1/2)²)3/2
(मं्ट उत्ततन)
/2
4Teol
6.
ip
-1/2
+ y?
V(z +1)2 +
Q
dr'
-1/2 V(x + x')² +(/2)-
1/2
dr'
7.
1/2
V(I + x')² + (!/2)²
Transcribed Image Text:Q (+')² + (1/2)²)3/2| 1/2 4TEol 1. (r+1)2+y I dz (r+)2+(1/2)² -1/2 1/2 4meol -1/2 H/2 dy -1/2 Q 2. 1 2Teol V(I+1)? + y² Q dy -1/2 (1² + y²)3/2' ((I + 1)2 + y²)3/2 3. 1/2 r' da 4Teol -1/2 /2 (+)2+(!/2)²)3/2 N/2 dy Q 4TEOl 4. +. (x2 + y²)3/2 ((x+1)2 + y²)3/2 (+x')dr' 1/2 ((x+')2+(!/2)²)3/2 4TEol N/2 dy (x² + y?)3/2 1 1 4TEOl 5. ((r +1)2 + y²)3/2 1/2 dr 4neol 1/2 ((* +x')² + (1/2)²)3/2 (मं्ट उत्ततन) /2 4Teol 6. ip -1/2 + y? V(z +1)2 + Q dr' -1/2 V(x + x')² +(/2)- 1/2 dr' 7. 1/2 V(I + x')² + (!/2)²
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