# Question on Calculating Coulomb force in VECTOR FORM

• mhrob24
In summary, you need to find the magnitude of the force vector, and then use Coulomb's law to find the unit vector.
mhrob24
Homework Statement
Point charges q1 = 14 µC and q2 = −60 µC are fixed at r1 = (5.0î − 4.0ĵ) m and r2 = (9.0î + 7.5ĵ) m.

What is the force (in N) of q2 on q1?
Relevant Equations
F = ke(Qq/r^2)
The only thing tripping me up here is that the answer needs to be in vector form. If the question was asking for the scalar form, then I would just find the distance between the charges (plot the charges according to their vector coordinates, then use pythagorean theorem to find the distance between the two. However, I believe (could be wrong here) that in order to get the vector form, I must calculate the force like I normally would for the scalar version, but then I would have to multiply the force by the unit vector representing the distance between the 2 charges. Here is my work done for this problem:

However, when I enter that vector at the bottom of my page into webassign (online HW platform), it is incorrect. I know the Force calculation is 100% correct so It has to be something with my unit vector, but I don't see the problem. The x-distance between the two charges is 4m and the y distance between the two charges is 11.5m right? So the vector representing the direct distance between the two charges is < 4.0, 11.5>. Then the unit vector is just this vector divided by its magnitude (sqrt(148.25)). I don't see where I'm going wrong...

I haven't checked any of the arithmetic. But, without doing any calculation, you should be able to deduce the signs of the x and y components of the force.

mhrob24
Lmao. You're right. My signs of the components of the force vector were backwards. Q2 will attract Q1 so Q1 will accelerate in both the POSITIVE x and y directions. I had both components of the force vector as negative. I switched the signs and got the correct answer on Webassign. I spent like an hour trying to figure out what was going on Thank you!

TSny
Yes. When you express the force vector in terms of a magnitude and a unit vector in the direction of the force, the magnitude part should be a positive number. When finding the magnitude of the force, just use the magnitudes (absolute values) of the charges in Coulomb's law.

## 1. What is Coulomb's Law and how is it related to calculating Coulomb force in vector form?

Coulomb's Law is a fundamental law in physics that explains the relationship between electric charges and the force between them. In vector form, Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

## 2. How do you calculate Coulomb force in vector form?

To calculate Coulomb force in vector form, you need to know the magnitude and direction of the charges and the distance between them. Then, you can use the formula F = (q1 * q2 / r^2) * r̂, where F is the force vector, q1 and q2 are the charges, r is the distance between them, and r̂ is the unit vector in the direction of the force.

## 3. What are the units of Coulomb force in vector form?

The units of Coulomb force in vector form are Newtons (N). This is because force is a vector quantity, and the unit for force is Newtons in the International System of Units (SI).

## 4. Can Coulomb force be repulsive as well as attractive?

Yes, Coulomb force can be either repulsive or attractive depending on the signs of the charges. Like charges (positive-positive or negative-negative) will repel each other, while opposite charges (positive-negative) will attract each other.

## 5. How does distance affect Coulomb force in vector form?

According to Coulomb's Law, the force between two charges is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases. This relationship is known as the inverse-square law.

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