Components of an electric field / charges

[scholio]

Homework Statement

four point charges are arranged at the corners of a square, as shown. a = 0.1m, q = 10^-3 coulombs

+1q
*
(+6q)* *(-3q)<-----------3a------------->P
*
+1q

an * indicates a point charge
the distance between each vertice is equal to 'a = 0.1m'
the y-axis is vertical, the x-axis is oriented horizontal

a) what is the y component of the electric field E at point P?

b) which charge, the +6q or the -3q gives the larger contribution to E at point P?

c) what is the force on a -12microcoulomb charge placed at point P?

Homework Equations

not sure with this one -- do i use pythagorean theorem?

E = kq/r^2 where E is electric field, k is constant 9*10^9, q is the charge, r is the distance

The Attempt at a Solution

for a) i think i find the net electric field of all four point charges using E = E1 + E2 + E3 + E4, but am not sure how to derive the y component, do i use the pythag theorem, do i use a/2 as the height, and (3a + a/2) for the base

i am confused now with how to use that to find the y component

any help with working throught this problem is greatly appreciated, asap please...

 

[AvroArrow]

for b) i think the +6q would give the larger contribution because it is the farthest away and the closer a charge is the lower the electric fieldfor c) F = qE so i would use the answer from a) for E

 

[Moetasim]

I would like to clarify a few things before providing a response. Firstly, it is important to note that the question does not specify the units for the distance 'a'. Assuming it is in meters, the four point charges can be represented as follows:

(+1q)-------(6q)-------(-3q)
| |
| |
| |
| |
| |
| |
(1q)-------(P)

The y-axis is vertical and the x-axis is horizontal. The distance between each charge and point P is 3a, which is equal to 0.3m.

a) To find the y component of the electric field at point P, we need to consider the individual contributions of each point charge. Using the formula E = kq/r^2, we can find the electric field due to each charge at point P. The y component of the electric field is given by the equation Ey = E sinθ, where θ is the angle between the electric field and the y-axis. In this case, since the electric field is acting in the positive y-direction, the angle θ is 90 degrees. Therefore, the y component of the electric field at point P is simply the magnitude of the electric field, which can be found by adding the individual contributions of the four point charges. This can be represented mathematically as Ey = E1y + E2y + E3y + E4y.

b) To determine which charge gives the larger contribution to the electric field at point P, we need to compare the magnitudes of the electric fields due to the +6q and -3q charges. Using the formula E = kq/r^2, we can find the electric field due to each charge. The charge with the larger magnitude will have a larger contribution to the electric field at point P.

c) To find the force on a -12 microcoulomb charge placed at point P, we can use the formula F = qE, where F is the force, q is the charge, and E is the electric field. Since we have already calculated the electric field at point P in part (a), we can simply plug in the values to find the force.

In conclusion, to solve this problem, we need to use the formula E = kq/r^2 to find the electric field due to each point charge at point