How Does Coulomb's Law Calculate Forces Between Two Point Charges?

[sushi362]

Homework Statement

Part 1:

A charge of 2 µC is at the origin, and a charge
of 6 µC is on the x-axis at x = 1 m.
Find the force on charge q2. The Colulomb
constant is 8.98755 × 10^9 N · m2/C2.

Answer in units of N

Part 2:

Find the force on q1.
Answer in units of N

Homework Equations

(Kc * Q2 * Q1)/R^2
Kc = 8.98x10^9

The Attempt at a Solution

So basically, for part one, i did..

(Kc * 2 * 6)/(1^2) = 1.07850E11
answer is positive so they should be repelling each other, but the program says its wrong, and I am not sure where to go for part 2.

Thanks.

 

[JonDrew]

When doing physics always, always mind your units, you should have put
-(Kc*2E-6*6E-6) / (1^2) = -0.108N

The second part should be the same answer, if not it will be the answer to Part 1 in its negated form (0.108N) or it will be basically the same equation with one of the point charges removed, i.e.

(Kc*q2) / (R^2)

But that is the expression for and electric field of a point charge, so Part 2 should just be the negative answer of part 1.

 

[sushi362]

When doing physics always, always mind your units, you should have put
(Kc*2E-6*6E-6) / (1^2) = 0.108N

The second part should be the same answer, if not it will be basically the same equation with one of the point charges removed, i.e. (Kc*q2) / (R^2) = F

What i don't understand is, my professor did a similar problem in class, except with 3 charges, and used the units in microcoloumbs and got the right answer? Or should i be doing all the problems in coloumbs instead?

 

[tms]

What i don't understand is, my professor did a similar problem in class, except with 3 charges, and used the units in microcoloumbs and got the right answer? Or should i be doing all the problems in coloumbs instead?

You should convert the charges to coulombs from micro coulombs. You can verify this by paying careful attention to the units, particularly the units of Coulomb's constant. If your teacher used micro coulombs, perhaps he had adjusted the constant beforehand; otherwise he couldn't have gotten the right answer.

 

[Nickie]

Part 1:

The force on q2 can be found using Coulomb's Law:

F = (Kc * q1 * q2)/r^2

Where:
Kc = Coulomb's constant = 8.98755 × 10^9 N · m2/C2
q1 = charge at the origin = 2 µC = 2 × 10^-6 C
q2 = charge on the x-axis = 6 µC = 6 × 10^-6 C
r = distance between the two charges = 1 m

Substituting the values in the equation, we get:

F = (8.98755 × 10^9 N · m2/C2 * 2 × 10^-6 C * 6 × 10^-6 C)/(1 m)^2
= 1.07850 × 10^11 N

Therefore, the force on q2 is 1.07850 × 10^11 N, in the direction away from q1, as expected.

Part 2:

Similarly, for the force on q1, we have:

F = (Kc * q1 * q2)/r^2

Where:
Kc = Coulomb's constant = 8.98755 × 10^9 N · m2/C2
q1 = charge at the origin = 2 µC = 2 × 10^-6 C
q2 = charge on the x-axis = 6 µC = 6 × 10^-6 C
r = distance between the two charges = 1 m

Substituting the values in the equation, we get:

F = (8.98755 × 10^9 N · m2/C2 * 2 × 10^-6 C * 6 × 10^-6 C)/(1 m)^2
= 1.07850 × 10^11 N

Therefore, the force on q1 is 1.07850 × 10^11 N, in the direction towards q2, as expected.