How Do You Calculate Bx in a Magnetic Field Problem Involving an Electron?

In summary, a magnetic field is a region in space where a magnetic force can be detected, created by moving electric charges in a specific direction. It has various practical applications, such as in generators and motors, and can be visualized and represented by a magnetic field matrix. When two magnetic fields are near each other, they can either attract or repel each other, based on their lines of force.
  • #1
sharris203
2
0

Homework Statement


An electron moves through a uniform magnetic field given by B = Bxi+(3.0Bx)j. At a particular instant, the electron has velocity v = (2.0i+4.0j)m/s and the magnetic force acting on it is (6.4x10-19N)k. Find Bx.

Homework Equations



Fb=|q|v x B

The Attempt at a Solution



B = Bxi + (3Bx)j + 0zk
v = 2xi + 4yj + 0zk
Fb = 0xi + 0yj + (6.4 * 10^[-19]N)k

I'm sure I need a matrix. But i can't figure it out, help!
 
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  • #2
solved.
 
  • #3


I would approach this problem by first identifying the known variables and equations that can be used to solve for the unknown variable, Bx.

Known variables:
- Magnetic field, B = Bxi + (3.0Bx)j
- Velocity, v = (2.0i + 4.0j)m/s
- Magnetic force, Fb = (6.4x10^-19N)k

Equation:
- Fb = |q|v x B

Now, using the equation Fb = |q|v x B, we can set up a matrix to solve for Bx.

| Fbx | | 0 | | Bx | | 0 |
| Fby | = | 0 | x | By | = | 0 |
| Fbz | | 6.4x10^-19 | | Bz | | (6.4x10^-19N) |

Since we are only interested in solving for Bx, we can focus on the first row of the matrix. Using the cross product formula, we can rewrite the first row as:

Fbx = -qvyBz + qvzBy

Since the electron has no z-component of velocity (vz = 0), the equation simplifies to:

Fbx = qvyBz

Solving for Bx, we get:

Bx = Fbx / (qvz)

Plugging in the known values, we get:

Bx = (6.4x10^-19N) / (1.6x10^-19C)(4.0m/s)

Bx = 1.0T

Therefore, the magnetic field in the x-direction is 1.0 Tesla.
 

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as electrons, and can be represented by lines of force.

How is a magnetic field created?

A magnetic field is created by moving electric charges, such as electrons, in a specific direction. This can happen naturally, as with the Earth's magnetic field, or it can be artificially created through the use of magnets or electric currents.

What is the purpose of a magnetic field?

Magnetic fields have many practical applications, such as in generators and motors, where they can convert mechanical energy into electrical energy and vice versa. They also play a crucial role in the function of electronic devices, such as computers and phones.

What is a magnetic field matrix?

A magnetic field matrix is a way of visualizing and representing the strength and direction of a magnetic field. It is often used in scientific research and engineering to better understand and manipulate magnetic fields.

How do magnetic fields interact with each other?

When two magnetic fields are near each other, they can either attract or repel each other depending on the direction of their lines of force. This interaction is described by the laws of magnetism and is the basis for many technological applications.

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