How Do You Calculate Electric Field and Potential at Specific Points?

[Tsar_183]

I have two questions, if i may ask. Really confusing stuff.

1. Three positive charges are arranged as shown (diagram is of a square). The Couloumb Constant is 8.99x10^9 N*m^2/C^2.

View attachment Nhein.bmp

Find the magnitude of the electric field at the 4th corner. Answer in units of N/C.


I'm pretty sure i need these equations for this problem.

Pythagorean Theorem:
z^2 = x^2 + y^2 --> or for a square: z^2 = (2d^2)

Electric Field Strength Equation:
E = (K)(q)/(d)^2
E = Electric Field Strength
K = Couloumbs Constant
q = Charge
d = Distance

3 Directions:
X - Direction
Y - Direction
(X,Y) or Z - Direction

So I did this with my vectors -
E(x) = (8.99 x 10^9 N*m^2/C^2)(1.0 nC x 10^-9 C/nC)/(.10m)^2
E(y) = (8.99 x 10^9 N*m^2/C^2)(3.0 nC x 10^-9 C/nC)/(.10m)^2
E(z) = (8.99 x 10^9 N*m^2/C^2)(1.0 nC x 10^-9 C/nC)/(SQRT((.10m)^2 +
(.10m)^2))

However i am unsure on the 3rd Vector, and on what to do next, do i add the 3 parts together to find the total or what?


2. Consider charges placed on the corner of a rectangle: let K = 8.98755 N*m^2/C^2 and g = 9.8 m/s^2.

View attachment Yen-Xi.bmp

Find the Electric Potential at the 4th point due to the grouping of charges at the other corners of the rectangle. Answer in units of V.

OK, well yeah here is my equations that i thought might help:

F = (m)(g)
m = mass
g = gravity due to acceleration

V = (E)(d) = (F)(d)/(q)
V = Volts
E = Electric Field Strength
F = Force
d = distance
q = charge

E = (K)(q)/(d)^2
E = Electric Field Strength
K = Couloumbs Constant
q = Charge
d = Distance

3 Directions:
X - Direction
Y - Direction
(X,Y) or Z - Direction

Well i thought about using the first equation to find the forces of each vector, but that didnt work out as i have no mass to use. Was the gravity of acceleration just a trick piece to hinder me? Haha I am unsure on that. If i use the second equation as is, I don't have a force, and the third equation will give me Electric Field Strength. Is there a mass that i need to answer this question? Force is my biggest issue here.

 

[christianjb]

to answer part of your question...

The field E, is just the force per unit charge. You add vectors of force to get the total force, so you add all the E vectors together to get the total force per unit charge at r.

The total force on a charge (if any) at r, is charge*force per unit charge, which is summarized as F=qE

Also- it's probably best not to use z as notation for your vector in the diagonal direction. x,y,z almost always implies that z is orthogonal to x and y.

 

[Tsar_183]

that should help, thanks :)