How Do You Calculate Magnetic Force in Three Dimensions?

In summary, magnetic force is a fundamental force of nature that causes attraction or repulsion between magnetic objects. It can be calculated using the formula F = qvBsinθ and acts on moving electric charges. It differs from electric force, which acts on both moving and stationary charges. The strength of magnetic force decreases with distance according to the inverse square law. Magnetic force has various real-world applications, including electric motors, generators, and MRI machines.
  • #1
EvaBugs
19
0
Hello.

I am currently working on this problem:
"An electron moves in the X-Y plane with a velocity v = (5 *10^5 m/s , 30 degrees). The uniform magnetic field i the region is B= ( 6 i - 2 j + 1 k ). Find the resultant magnetic force on the electron in component form."

I know that F = qv x B = qvB sin (teta)

What mixes me up is the fact that B has 3 components. How should I begin?
 
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  • #2
You could begin by writing v in terms of it's 3 components. Then do the cross product.
 
  • #3


Hello there,

Thank you for reaching out for help with this problem. It seems like you have a good understanding of the formula for calculating the magnetic force on a moving charged particle. You are correct in using the formula F = qv x B = qvB sin (teta).

In this case, the magnetic field B has three components, which can be written as (6, -2, 1). In order to find the resultant magnetic force on the electron, we can break down the formula into its component form. This means we will calculate the x, y, and z components of the force separately and then add them together to find the total force.

Starting with the x component, we have qvB sin (teta) = (1.6 * 10^-19 C)(5 * 10^5 m/s)(6 T)(sin 30 degrees) = 2.4 * 10^-14 N. This is the force acting in the x direction.

Similarly, for the y component, we have qvB sin (teta) = (1.6 * 10^-19 C)(5 * 10^5 m/s)(-2 T)(sin 30 degrees) = -8 * 10^-15 N. This is the force acting in the y direction.

Lastly, for the z component, we have qvB sin (teta) = (1.6 * 10^-19 C)(5 * 10^5 m/s)(1 T)(sin 30 degrees) = 4 * 10^-15 N. This is the force acting in the z direction.

To find the total force, we simply add these components together, giving us a resultant magnetic force of (2.4 * 10^-14 N, -8 * 10^-15 N, 4 * 10^-15 N). This is the force acting on the electron in the X-Y plane with a velocity of (5 * 10^5 m/s, 30 degrees).

I hope this helps you understand how to approach this problem. Good luck with your calculations!
 

Related to How Do You Calculate Magnetic Force in Three Dimensions?

1. What is magnetic force?

Magnetic force is a fundamental force of nature that is responsible for the attraction or repulsion between magnetic objects.

2. How do you calculate magnetic force?

Magnetic force can be calculated using the formula F = qvBsinθ, where q is the charge of the object, v is the velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field.

3. What is the difference between magnetic force and electric force?

The main difference between magnetic force and electric force is that magnetic force acts on moving electric charges, while electric force acts on both moving and stationary charges.

4. How does distance affect magnetic force?

According to the inverse square law, the strength of magnetic force decreases as the distance between two objects increases. This means that the closer two objects are, the stronger the magnetic force between them will be.

5. What are some real-world applications of magnetic force?

Magnetic force has many practical applications, such as in electric motors, generators, MRI machines, and compasses. It is also used in industries like manufacturing, transportation, and energy production.

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