Download An electric dipole is formed from ±5.0 nC point charges spaced 2.0

An electric dipole is formed from ±5.0 nC point charges spaced 2.0 mm apart. The dipole is
centered at the origin, oriented along the y-axis with the positive charge above the x-axis.
What is the electric field at point (x,y) = (10 cm, 0 cm)?
What is the electric field at point (x,y) = (0 cm, 10 cm)?
We can make the following figure.
Electric field at (10, 0) =?
The distance between each charge location and (10, 0) = 102  0.12  100.01 cms.
If field at (10, 0) due to each dipole charge is E, we will have
E
tan  
5 109  9 109
 100.01 


 100 
2
45 1002

 4499.55 N/C
100.01
0.1
   0.572940
10
Hence, field at (10, 0) = 2 E cos   2  4499.55cos 0.572940  8998.65 N/C in x-direction.
Electric field at (0, 10) =?
Distance between 5nC charge and (0,10) = 10-0.1 = 9.9 cms.
Distance between -5nC charge and (0,10) = 10+0.1 = 10.1 cms.
Field at (0, 10) at +ve due to 5nC charge = 
5 109  9 109
 9.9 
100 
2
ay 
45 1002
a y  4591.368a y N/C
9.92
Field at (0, 10) at +ve due to -5Nc charge  
5 109  9 109
10.1
 100 
2
Hence, total field at (0,10) = (4591.368 – 4411.33)ay N/C
= 180.038ay N/C
45 1002
ay  
a y  4411.33a y N/C
10.12