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41
The plastic rod at right has charge +Q 
uniformly distributed along its length L.  Find 
the electric field at all points on the x-axis to the 
right of the rod.  
Mathematical Analysis 
Carefully identify and label “s” the location of the differential element on the diagram above. 
Carefully identify and label “x” the location of the point of interest on the diagram above.  
Write an expression for dq, the charge on the differential element. 
Write an expression for r, the distance between the differential element and the point of interest. 
Write an expression for , the unit vector representing the direction from the element to the point of interest. 
Write an integral expression for the electric field. Choosing limits of integration, calculate the integral. 
Questions 
At x = L/2, what should E
x
equal? Does your function agree with this observation? 
If x >> L, what should E
x
equal? Does your function agree with this observation? 
rˆ
ˆ
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42
The plastic rod at right has charge -Q uniformly 
distributed along its length L. Find the electric 
field at all points on the y-axis above the rod.  
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43
The very long plastic rod at right has uniform 
charge density +2.0 nC/m 
along its length. Find 
the electric field 10 cm above the center of the 
rod. 
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44
The 15 cm plastic rod at right has 2.5 nC 
distributed uniformly along its length. Find the 
electric field at the point (x, y) = (0, 5.0 cm).  
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45
The 10 cm plastic rod at right has uniform 
charge density –3.5 pC/m. Find the electric 
field at the point (x, y) = (-5.0 cm, 0). 
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46
The plastic rod at right extends from y = -2a to y = a and has charge Q 
uniformly distributed along its length. Find the electric field at the point 
(x, y) = (2a, 0). 
47
The plastic rod at right forms a quarter-circle of radius R and has uniform 
charge density +
 Find the electric field at the origin. 
48
The plastic rod at right forms a half-circle and has charge -Q uniformly 
distributed along its length L.  Find the electric field at the origin. 
49
The plastic rod at right forms a three-quarter-circle of radius R and has 
uniform charge density +
.  Find the electric field at the origin. 
50
The plastic rod at right has charge +Q 
uniformly distributed along its length L.  In 
order to find the electric field at all points on the 
x-axis to the right of the rod, four different 
location labels are used for the differential 
element. For each location label, write the 
correct integral expression, including limits, for 
the electric field. 
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