# Three Point Charges, find the electric force exerted

• m00nbeam360
In summary: Overall, the summary of the conversation is: "In summary, three charges of magnitude 2 nC are arranged in a square with two positive charges at opposite corners and one negative charge at the remaining corner. The force exerted by these charges on a fourth charge of +3 nC at the upper right corner can be found using the equation F4 = F1,4 + F2,4 + F3,4, where k = 8.988*10^9 N*m^2/C^2 and F1,4 = F2,4 = 3.595 * 10^-4 j. The calculation for F3,4 may have been incorrect due to a mistaken value for q4. Further review and
m00nbeam360

## Homework Statement

Three charges, each of magnitude 2 nC, are at separate corners of a square of edge length 1 cm. The two charges at opposite corners are positive, and the other charge is negative. Find the force exerted by these charges on a fourth charge q = +3 nC at the remaining (upper right) corner. (Assume the +x axis is directed to the right and the +y axis is directed upward.)

## Homework Equations

k = (8.988*10^9 N*m^2/C^2)

## The Attempt at a Solution

Drew a diagram of the problem such that F4 = F1,4 + F2,4 + F 3,4.

F1,4 = (k*q1*q4)/(r(1,4)^2)j

F1,4 = (8.988*10^9 N*m^2/C^2)(2.00*10^-9)*((2.00*10^-9)/(0.01m)^2)

= 3.595 * 10^-4 j

F2,4 = same

F3,4 = (k*q1*q2)/(r(2,4)^2)*r(3,4)

r(3,4) = r(3,1) + r(1,4) = (0.01m)i + (0.01m)j

r(3,4) = (0.01m)i+(0.01m)j/(sqrt(0.01m^2+0.01m^2)) = 0.14i + 0.14j

F3,4 = (8.988*10^9) (-2.00*10^-9)(2.00*10^-9)/(0.01sqrt(2)^2)*(0.14i+0.14j)

= -2.52 * 10 ^ -5

(3.595 * 10^-4) i - (-2.52*10^-5) i = 3.34*10^-4i <--- Wrong :(
(3.595 * 10^-4) j - (-2.52*10^-5) j = 3.34*10^-4j <--- Wrong :(

Any suggestions?? I think that somewhere in computing F3,4 I put in an incorrect number. Thanks!

m00nbeam360 said:
r(3,4) = (0.01m)i+(0.01m)j/(sqrt(0.01m^2+0.01m^2)) = 0.14i + 0.14j

Check this.

Whoa, got .707 now, thanks. So then is everything else correct?

m00nbeam360 said:
F1,4 = (k*q1*q4)/(r(1,4)^2)j

F1,4 = (8.988*10^9 N*m^2/C^2)(2.00*10^-9)*((2.00*10^-9)/(0.01m)^2)

= 3.595 * 10^-4 j

Did you use the correct value for q4 here?

Your attempt at solving the problem is correct. The mistake may be in your calculations. Make sure to check your units and that you are using the correct values for the charges and distances. Also, double check your calculations for F1,4 and F2,4. If the problem persists, try solving the problem again and see if you get the same answer. If not, you may need to seek help from a classmate or your instructor.

## 1. What is the formula for finding the electric force exerted by three point charges?

The formula for finding the electric force exerted by three point charges is F = k(q1q2/r1² + q1q3/r2² + q2q3/r3²), where k is the Coulomb's constant, q1, q2, and q3 are the charges of the three point charges, and r1, r2, and r3 are the distances between each pair of charges.

## 2. How do you determine the direction of the electric force exerted by three point charges?

The direction of the electric force exerted by three point charges can be determined by using the principle of superposition. This means that the direction of the net electric force is the vector sum of the individual electric forces exerted by each charge.

## 3. What is the unit of measurement for electric force?

The unit of measurement for electric force is Newtons (N).

## 4. Can the electric force exerted by three point charges be repulsive or attractive?

Yes, the electric force exerted by three point charges can be both repulsive and attractive. The force is repulsive when the charges have the same sign, and attractive when the charges have opposite signs.

## 5. How does increasing the distance between the three point charges affect the electric force exerted?

Increasing the distance between the three point charges decreases the electric force exerted. This is because the force is inversely proportional to the square of the distance between the charges, according to the formula F = k(q1q2/r²).

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