Force on a wire, by a current carrying wire.

In summary, the conversation discusses the calculation of the magnitude of force per unit length between two wires, one with a constant charge density and the other with a constant current. The formula F=BIL is used, but there is confusion about how to incorporate the charge density into the equation. The conversation also mentions the types of fields created by charge density and current, and the sources of these fields. The final question asks about the forces between these fields and their respective sources. Ultimately, the conversation revolves around understanding the relationship between charge, current, and force in regards to magnetic and electric fields.
  • #1
bfusco
128
1

Homework Statement


What is the magnitude of the force per unit length on a long wire of charge density λ from a wire that carries a current of 3 A and is a distance of 3 m away?
A)μλ/2 B)μλ/6 C)3μλ/2 D)μλ/3 E)0

The Attempt at a Solution


F=BIL→ (F/L)=BI →(F/L)=μI1I2L/2∏R

I don't know how to apply that λ. i would think that λ=Q/L, and i also don't know which current is which in that final equation i put (that may be a slightly tangential question, but i also need help understanding which is which if one could aid with that).
 
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  • #2
You have one wire with a constant charge density λ, and another with a constant current 3A. They are 3m apart. What is the force between them.
What kind of field does a charge density create?
What kind of field does a current create?
What are the forces between one wire's field and another wire's source?
 
  • #3
frogjg2003 said:
You have one wire with a constant charge density λ, and another with a constant current 3A. They are 3m apart. What is the force between them.
What kind of field does a charge density create?
What kind of field does a current create?
What are the forces between one wire's field and another wire's source?

-a charge density doesn't create a field, the charge needs to be moving to generate a magnetic field.
-a current creates a field that circles the wire radially, either clockwise of counterclockwise depending on the direction of the current. But there is no indication of the direction the wires sit with respect to each other, neither parallel nor perpendicular.
-considering what this question is giving, there is no reference to a wire's source (which I am guessing you mean voltage?)
 
  • #4
bfusco said:
-a charge density doesn't create a field, the charge needs to be moving to generate a magnetic field.
Charges create electric fields, moving or not.
-considering what this question is giving, there is no reference to a wire's source (which I am guessing you mean voltage?)
Charges are the sources of electric fields. Currents are the sources of magnetic fields.
My question could be better stated as:
What is the force of a Magnetic field on a charge?
What is the force of an Electric field on a current?
 
  • #5


I would approach this problem by first clarifying some key concepts. The force on a wire is due to the interaction between the magnetic fields produced by the two wires. The force per unit length is the force experienced by a small segment of the wire, and we can calculate this by dividing the total force by the length of the wire.

Next, I would use the equation F = BIL to calculate the force between the two wires. B is the magnetic field, I is the current, and L is the length of the wire. In this case, we have two wires, so we need to consider the force produced by each wire on the other.

To incorporate the charge density, we can use the equation λ = Q/L, where Q is the total charge on the wire and L is the length of the wire. We can substitute this into the equation for B, which becomes B = μIλ/2πR, where μ is the permeability of free space and R is the distance between the two wires.

Finally, we can put everything together to get F/L = (μI1I2λ/2πR)/L = μI1I2λ/2πRL. We know that I1 = 3 A, I2 = 0 (since the second wire is not carrying any current), λ = Q/L, and R = 3 m. Plugging in these values gives us F/L = 3μQ/2πL^2.

To determine the correct answer, we need to remember that the magnitude of the force per unit length is a positive value, and it is given by the absolute value of the equation above. Therefore, the correct answer is C) 3μλ/2. This is because the magnitude of the current in the second wire is 0, so we can ignore it in the equation. The force per unit length is directly proportional to the charge density, so the answer is 3 times larger than the force per unit length if the second wire was also carrying a current of 3 A.
 

1. What is force on a wire caused by a current carrying wire?

The force on a wire, also known as the magnetic force, is caused by the interaction between the magnetic field generated by the current carrying wire and the magnetic field of the wire itself.

2. How is the force on a wire calculated?

The force on a wire is calculated using the formula F = I x L x B, where I is the current flowing through the wire, L is the length of the wire, and B is the magnetic field of the wire.

3. What is the direction of the force on a wire?

The direction of the force on a wire is determined by the right-hand rule, where the thumb points in the direction of the current, the fingers point in the direction of the magnetic field, and the palm indicates the direction of the force.

4. How does the force on a wire change with the strength of the current?

The force on a wire is directly proportional to the strength of the current. This means that as the current increases, the force on the wire also increases. Similarly, if the current decreases, the force on the wire decreases.

5. What are some practical applications of the force on a wire from a current carrying wire?

The force on a wire is used in various technologies, such as motors, generators, and speakers. It is also used in particle accelerators and in the production of magnetic levitation trains. Additionally, the force on a wire is essential in the study of electromagnetism and is used in many scientific experiments.

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