Electrostatic Force and Field between two charges

In summary: You need a vector to represent the force.In summary, two positive point charges with a charge of 10nC each are 10cm apart. The electric field strength at point A is zero due to the opposing components of the field. For the second part, if a charge of 100nC is placed at point A, the resulting force is 25,43* 10^-3 N directed in the positive y direction. It is important to use proper vector addition and unit vectors when calculating the electric field strength and force.
  • #1
psy
13
1
Two positive point charges with a charge of 10nC each are 10cm apart. What is the electric field strength at point A? How is it directed? Which force acts on a charge of 100nC at point A?
upload_2018-5-6_14-55-39.png
F = k * q1 * q2 / r^2
E = F/q
r^2 = (l1/2)^2 + (l2)^2 => r = 0,707m

Electric field strength :

E1 = E2 = 8.99 x 10^9 Nm^2/C^2 * 10*10^-9C / (0,707m)^2 = 179,854 N/C So i "pulled apart" the Electric field strength in x and y components.
upload_2018-5-6_15-39-14.png

E1y = E1 * cos(45°)= 127,176 N/C
E2y = E2 * cos(45°)=127,176 N/C
E1x = E1 * sin(45°) = 127, 176 N/C
E2x = E2* sin(45°) = 127, 176 N/C

As the Field strength components have the same Amount, yet oppose direction they substract themselvs to Zero, E1y-E2y = 0 ; E1x-E2x = 0. So the Overall Field strength in Point A is Zero.

At the second part i suppose to calculate the Electric Force, if at Point A is a Charge q3= 100nC.
Fe1 = k * q1 * q3 / r^2 = 1,7985*10^-5 N
Fe2 = k * q1 * q3 / r^2 = 1,7985*10^-5 N.

The Overall force Fe^2 = Fe1^2 + Fe2 ^2 => Fe = 2,54 * 10^-5.

Is this the right way to calculate it? I am open for every Suggestion.

Kind Regards
 

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  • #2
psy said:
As the Field strength components have the same Amount, yet oppose direction they substract themselvs to Zero, E1y-E2y = 0 ; E1x-E2x = 0. So the Overall Field strength in Point A is Zero.
I can see that E1x and E2x are opposite and add to zero. Why do the y components add to zero? There is a problem in how you are treating the components. The components of a vector are algebraic quantities. E1x and E2x do not have the same sign.
For the second part, the two forces on the point charge at the point A are vectors. They should be added as vectors. You added their magnitudes. Your diagram is showing the forces correctly, but you did ot follow it up with the correct method of vector addition.
 
  • #3
Hello

So i have made the following correction:

r= 0,0707m

E1 = E2 = 17985,4 N/C

E1y = E1 * cos(-45°)= 12717,6 N/C
E2y = E2 * cos(45°)=12717,6 N/C
E1x = E1 * sin(-45°) = -12717,6 N/C
E2x = E2* sin(45°) = 12717,6 N/C

Ey = E1y+E2y = 25435.2 N/C
Ex = E1x+ E2x = -12717,6 N/C+12717,6 N/C = 0.

So the Electric field strength is E = Ey + Ex = 25435.2 N/C + 0 = 25435.2 N/C

In the second part, for calculating the force in case there is a 100nC Point Charge at the given spot :

F= q*E =100*10^-9C * 25435.2 N/C = 25,43* 10^-3 N.

Is this the correct way?

Kind Regards
 
  • #4
You should really read up about how to add and subtract vectors from your textbook. For any vector V (bold font)
V ≠ Vx + Vy
The left hand side is a vector, with a direction. The components on the right hand side are not vectors. They are algebraic quantities. You must use either unit vectors, or specify both magnitude and direction to write a vector.
 
  • #5
IEI = sqrt( Ey^2 + Ex^2) = 25435.2 N/C ?
 
  • #6
And the direction. Same with the force.
 

1. What is electrostatic force?

Electrostatic force is the force that exists between two electrically charged particles. It can be attractive or repulsive, depending on the charges of the particles.

2. How is electrostatic force calculated?

Electrostatic force is calculated using Coulomb's law, which states that the force (F) between two charges (q1 and q2) separated by a distance (r) is equal to the product of the charges divided by the square of the distance (ke is a proportionality constant):
F = ke * (q1 * q2) / r2

3. What is an electric field?

An electric field is a region of space surrounding a charged particle, where the force acting on another charged particle is influenced by the presence of the first charged particle. It is represented by lines of force that point in the direction of the force that would act on a positive test charge placed in the field.

4. How is electric field strength calculated?

Electric field strength is calculated by dividing the force acting on a test charge (qt) by the magnitude of the test charge (qt):
E = F / qt

5. How does distance affect the strength of electrostatic force and field?

The strength of electrostatic force and field decreases as the distance between two charged particles increases. This is because the force and field are inversely proportional to the square of the distance (as seen in Coulomb's law and the formula for electric field strength). As the distance increases, the force and field become weaker, and eventually become negligible when the distance is very large.

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