Long straight wire: Ampere/Biot Savart

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In summary, By using the Biot-Savart law and the Lorentz force law, the magnitude and direction of the force acting on an electron moving parallel to a 2.0A current-carrying wire at a distance of 0.01m with a velocity of 100ms-1 can be calculated to be 6.32x10-22 N radially away from the wire. However, the direction could also be towards the wire depending on the relative direction of the current and velocity.
  • #1
Roodles01
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Homework Statement


A long straight wire carries a current of 2.0A. An electron moves parallel to it at a distance of 0.01m (I'm assuming id doesn't matter which way it moves) at a velocity, v = 100ms-1
Calculate magnitude & direction of force acting on it.

Homework Equations


B = μ0 L / 2∏r

F = q(v X B)

I know the second is the Lorentz force law & that the first relates to Biot-Savart but for the Biot-Savart I also have,
F12 = μ0/4∏ * I1 δl1 * ( I2 δl2 * rhat 12) / r122

So how does one relate to the other, please.

The Attempt at a Solution



Surely it can't be this easy!

B = μ0 L / 2∏r
B = 4∏x10-7 * 2.0 / 2∏(0.01)
B = 3.95x10-8 T

F = q(v X B)
F = (-1.6x10-19)(100x103)(3.95x10-8
F = -6.32x10-22 N

Magnitude 6.32x10-22 N
Direction (radially) away from wire
 
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  • #2
Roodles01 said:

Homework Statement


A long straight wire carries a current of 2.0A. An electron moves parallel to it at a distance of 0.01m (I'm assuming id doesn't matter which way it moves) at a velocity, v = 100ms-1
Calculate magnitude & direction of force acting on it.


Surely it can't be this easy!

B = μ0 L / 2∏r
B = 4∏x10-7 * 2.0 / 2∏(0.01)
B = 3.95x10-8 T

F = q(v X B)
F = (-1.6x10-19)(100x103)(3.95x10-8
F = -6.32x10-22 N

Magnitude 6.32x10-22 N
Direction (radially) away from wire

Surely it can!
Except the direction could be towards or away from the wire, depending on the relative direction of v and i and the position of q.

BTW I've never seen L used for current before ...
 
  • #3
L . . . oops!
 

What is the Ampere's law?

The Ampere's law is a fundamental law in electromagnetism that describes the relationship between an electric current and the magnetic field it produces. It states that the magnetic field created by a long straight wire is directly proportional to the current passing through the wire and inversely proportional to the distance from the wire.

What is the Biot-Savart law?

The Biot-Savart law is a mathematical equation that describes the magnetic field created by a current-carrying wire. It states that the magnetic field at a point in space is proportional to the current, the length of the wire, and the sine of the angle between the wire and the point. It is often used to calculate the magnetic field around a long straight wire.

How do you calculate the magnetic field of a long straight wire using Ampere's law?

To calculate the magnetic field of a long straight wire using Ampere's law, you need to know the current passing through the wire, the distance from the wire, and the permeability of the medium surrounding the wire. You can then use the formula B = μ0I/2πr, where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

How does the magnetic field of a long straight wire change with distance?

The magnetic field of a long straight wire decreases as the distance from the wire increases. This is because the Biot-Savart law states that the magnetic field is inversely proportional to the distance from the wire. This means that the further away from the wire you are, the weaker the magnetic field will be.

What are some real-life applications of Ampere's law and the Biot-Savart law?

Ampere's law and the Biot-Savart law have many real-life applications, such as in the design of electromagnets, motors, and generators. They are also used in medical imaging techniques such as magnetic resonance imaging (MRI). These laws are also important in understanding the behavior of Earth's magnetic field and how it affects our daily lives.

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