Rod of current wire exerting magnetic force on current carrying bar

In summary, a thin copper bar of length 14.0 cm is supported horizontally and carries current I1 = 105 A in the -x direction. At a distance h = 0.500 cm below one end of the bar, a long straight wire carries a current I2 = 200 A in the z direction. Using the Biot-Savart Law and the equation for magnetic force, we can calculate the magnitude and direction of the magnetic force exerted on the bar. The magnetic force is perpendicular to both the current element ds and the magnetic field, which varies over the length of the bar and must be integrated to find the overall force.
  • #1
JosephK
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Homework Statement


Figure is attached.

A thin copper bar of length = 14.0 cm is supported horizontally by two (nonmagnetic) contacts. The bar carries current I1 = 105 A in the -x direction, as shown in the figure below. At a distance h = 0.500 cm below one end of the bar, a long straight wire carries a current I2 = 200 A in the z direction. Determine the magnitude and direction of the magnetic force exerted on the bar.


Homework Equations



I = μI/2∏r
F = IL X B

The Attempt at a Solution



By the Biot-Savart Law, a magnetic field is created by a current carrying wire. Because the wire carries a current I, there is a magnetic field in the region. Since the wire is long, we may assume infinite length. The magnetic field of an infinite wire length r away we calculated B = μI/2∏r.


From the classroom demonstration we learned a current carrying wire in a magnetic field experiences a magnetic force. The magnetic force is perpendicular to both current element ds and B. The force experienced by the rod is F = ILXB. Since B varies over the length of the bar, we need to integrate. Also, the appropriate equation to use is dF = I dsXB since the angle between ds and B vary as well. After combining the equation for B and replacing theta in terms of r and integrating should I have the answer?

 

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  • #2
I'm really confused, I've been trying to figure out this problem for hours! Any help would be greatly appreciated.
 

1. How does a rod of current wire exert magnetic force on a current carrying bar?

When a current-carrying wire is placed near a current-carrying bar, it creates a magnetic field. This magnetic field exerts a force on the bar, causing it to move. The direction of the force is determined by the right-hand rule, where the thumb points in the direction of the current flow and the fingers curl in the direction of the magnetic field.

2. What factors affect the strength of the magnetic force?

The strength of the magnetic force is influenced by the amount of current flowing through the wire, the distance between the wire and the bar, and the orientation of the wire and bar in relation to each other. Additionally, the material of the wire and bar can also affect the strength of the force.

3. Can the direction of the magnetic force be reversed?

Yes, the direction of the magnetic force can be reversed by changing the direction of either the current in the wire or the magnetic field. If the current is reversed, the force will also reverse. Similarly, if the orientation of the wire and bar is changed, the force will also change direction.

4. What is the purpose of the rod of current wire in this scenario?

The rod of current wire is used to create a magnetic field that exerts a force on the current-carrying bar. This can be useful in a variety of applications, such as in motors and generators where the force can be used to create motion.

5. Are there any safety precautions to consider when working with a rod of current wire and a current-carrying bar?

Yes, it is important to ensure that the currents in the wire and bar are not too high, as this can cause excessive heating and potential hazards. It is also important to be aware of any potential electromagnetic interference that may affect nearby electronic devices. Proper insulation and grounding of the circuit are also important safety considerations.

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