physics question 1

Question

Determine magnitude of the electric field at the point P shown in the figure. The two charges are separated by a distance of 2  from the midpoint between them. Point P is on the perpendicular bisector of the line joining the charges, a distance 

 from the midpoint between them.

https://session.masteringphysics.com/problemAsset/1737355/1/GIANCOLI.ch21.p48.jpg

Answer 1

Draw a picture of the two electric field vectors at P (from the two charges) and note that the net field must point in the negative vertical direction. The fields from the two charges have the same magnitude, so it is sufficient to find the vertical component of one field, multiply it by 2, and point it in the negative vertical direction. Assuming the vertical axis is the y-axis, define

sinθ = a / √(x² + a²)

Then

E = 2E_y = 2[kQ / (x² + a²)] sinθ

E = 2[kQ / (x² + a²)] [a / √(x² + a²)]

E = 2kQa / (x² + a²)^3/2