How Can I Solve Question Type: "With Magnitude and Unit Vectors"?

• denfaro
In summary, the conversation discusses the concept of vectors and their use in solving a question about charged spheres. The participants also mention Coulomb's Law and the importance of including direction in the calculation of force between charges.
denfaro
Hi I am a beginner in this topic. I didn't understand this question type clearly.What does it mean" With Magnitude and Unit Vectors" exactly? May you help me for the solution step by step :). Thanks in advance.

denfaro said:
Hi I am a beginner in this topic. I didn't understand this question type clearly.What does it mean" With Magnitude and Unit Vectors" exactly? May you help me for the solution step by step :). Thanks in advance.
View attachment 260846
Welcome to the PF.

We cannot do your schoolwork/homework for you, but perhaps we can give you a few tips to help your understanding so that you can start working on the problem.

What have you done with vectors so far? You know that vectors have a magnitude and direction, right? And have you learned about coordinate systems like Caretesian coordinates, where there are x and y directions, etc.?

berkeman said:
Welcome to the PF.

We cannot do your schoolwork/homework for you, but perhaps we can give you a few tips to help your understanding so that you can start working on the problem.

What have you done with vectors so far? You know that vectors have a magnitude and direction, right? And have you learned about coordinate systems like Caretesian coordinates, where there are x and y directions, etc.?
Yes I learned the vectors,coordinate system but I don't know how can I use them on this question.

denfaro said:
Yes I learned the vectors,coordinate system but I don't know how can I use them on this question.
So start by drawing an x-y set of axes on the diagram. I would probably make the (0,0) point at the A charge, with the x-axis to the right and the y-axis pointing up.

Then write the general vector force equation for the force on one charge due the electric field from another charge (based on the amount of the charges and the separation distance).

Please do those things, and show us what you get. Thank you.

denfaro said:
Yes I learned the vectors,coordinate system but I don't know how can I use them on this question.
Do you know charged spheres will apply force on each other?

Do you know charged spheres will apply force on each other?
Yes I know

denfaro said:
Yes I know
What’s the expression for that force? I mean is there any law which governs how two charged spheres will apply force on each other ?

What’s the expression for that force? I mean is there any law which governs how two charged spheres will apply force on each other ?
I think you mean Coulmb's Law

denfaro said:
I think you mean Coulmb's Law
Yes. Can you please write out the Coulombs Law?

Yes. Can you please write out the Coulombs Law?
F=(k*(q1*q2))/r^2.

denfaro said:
F=(k*(q1*q2))/r^2.
But force is a vector quantity, the expression which you have given doesn’t involve the direction of the force. Can you fix it? Can you do something so that we get a vector quantity in that expression of Coulombs Law?

But force is a vector quantity, the expression which you have given doesn’t involve the direction of the force. Can you fix it? Can you do something so that we get a vector quantity in that expression of Coulombs Law?
Sorry I don't. How can I do that?

denfaro said:
Sorry I don't. How can I do that?
$$\vec{F} = k \frac{q_1 ~q_2 }{r^2}~ \hat{r}$$ the force acts on the line joining the two charges.

berkeman and denfaro
$$\vec{F} = k \frac{q_1 ~q_2 }{r^2}~ \hat{r}$$ the force acts on the line joining the two charges.
Thanks I have an idea now. :)

And it's important to remember that the force between like charges is repulsive, and the force between opposite charges is attractive. That's where the direction for the force vector comes from.

1. What is a magnitude vector?

A magnitude vector is a mathematical representation of a vector's length or size. It is typically denoted by ||v||, where v is the vector, and is calculated using the Pythagorean theorem.

2. What is a unit vector?

A unit vector is a vector that has a magnitude of 1 and is used to represent direction. It is typically denoted by a hat symbol (^) over the vector, such as â or ı̂. Unit vectors are important in vector calculations as they help to determine direction and can be used to scale other vectors.

3. How do I find the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In vector terms, this means that the magnitude of a vector ||v|| can be calculated as √(v1² + v2² + v3²), where v1, v2, and v3 are the components of the vector in each dimension.

4. How do I find the unit vector of a given vector?

To find the unit vector of a given vector, you first need to find the magnitude of the vector using the Pythagorean theorem. Then, divide each component of the vector by the magnitude to get the unit vector. For example, if the given vector is v = (3, 4, 5), the magnitude is √(3² + 4² + 5²) = √50. The unit vector would then be (3/√50, 4/√50, 5/√50).

5. How are magnitude and unit vectors used in physics and engineering?

Magnitude and unit vectors are used in many areas of physics and engineering, such as mechanics, electromagnetism, and fluid dynamics. They are used to represent physical quantities, such as force, velocity, and acceleration, and to perform calculations involving these quantities. In engineering, they are used to design and analyze structures and systems, such as bridges, buildings, and electrical circuits.

• Introductory Physics Homework Help
Replies
13
Views
496
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
55
• Introductory Physics Homework Help
Replies
3
Views
59
• Introductory Physics Homework Help
Replies
3
Views
408
• Introductory Physics Homework Help
Replies
13
Views
577
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
751