How Do You Calculate the Current in Each Wire When a Charge Moves Between Them?

In summary, the problem involves two infinitely long wires with currents running in the positive y direction and a charge moving in the positive y direction at a given distance from the first wire. The net force from both wires on the charge is in the negative x direction, and the goal is to find the current in each wire using the equations for magnetic field and force. By finding the individual magnetic fields from each wire and taking the difference, the current in each wire can be solved for.
  • #1
yankeekd25
27
0

Homework Statement


Two infinitely long wires are separated by a distance of d = 1.4 meters. Both have current running in the positive y direction. A charge of q = +2.7 micro-Coulombs is moving in the positive y direction at v = 3.1 E 6 m/s a distance of r = 0.22 meters from the wire on the left as shown in the diagram. The net force from both wires on the charge is in the x direction with a magnitude of 53 E -6 Newtons. What is the current in each wire in amps?

Two vertical wires. A charge q is .22 meters from the left wire. The Velocity vector is in the positive y direction, and the Fb vector is in the negative x direction, perpendicular to the velocity vector. The second vertical wire is 1.4 meters away from the first.

Homework Equations


Fb= qvb sin theta
B= u0 I / 2 pi r

The Attempt at a Solution


I know these two equations must be used, but I'm not sure what to do with both wires. Do I need to apply the charge to each of the wires and do something with that?

First, do I find B by doing B= Fb/ qv sin 90. Is this correct so far?

Thanks in advance.
 
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  • #2
Since the currents in the wires are in the same direction, magnetic field at any point between the two wires is the difference of the fields due to each wire.
You have written the expression for the net field B. Now find B1 and B2 at the given point.
Using B = B1 - B2, solve for the current.
 
  • #3
rl.bhat said:
Since the currents in the wires are in the same direction, magnetic field at any point between the two wires is the difference of the fields due to each wire.
You have written the expression for the net field B. Now find B1 and B2 at the given point.
Using B = B1 - B2, solve for the current.

Does B1 = u0 I / 2 pi r, where r is the distance from the point to wire 1, and B2 is the same, but with r= the distance from the charge to the second wire?
 
  • #4
yankeekd25 said:
Does B1 = u0 I / 2 pi r, where r is the distance from the point to wire 1, and B2 is the same, but with r= the distance from the charge to the second wire?
Yes.
 
  • #5
rl.bhat said:
Yes.

Thank you very much!
 

Related to How Do You Calculate the Current in Each Wire When a Charge Moves Between Them?

1. What is the current of wires and why is it important?

The current of wires refers to the flow of electric charge through a wire. It is important because it determines the amount of electricity that can be transmitted through a wire and is a crucial factor in determining the efficiency and safety of electrical systems.

2. How is the current of wires measured?

The current of wires is typically measured using an ammeter, which is a device that measures the amount of current flowing through a wire or circuit. The unit of measurement for current is amperes (A).

3. What factors affect the current of wires?

The current of wires can be affected by several factors, including the voltage of the power source, the resistance of the wire, and the temperature of the wire. Higher voltages and lower resistance will result in a higher current, while higher temperatures can decrease the current flow.

4. How can the current of wires be controlled?

The current of wires can be controlled by using devices such as resistors, which can limit the flow of current in a circuit. Additionally, the thickness and material of the wire can also affect the current flow. Thicker wires and materials with lower resistance can allow for a higher current to flow.

5. What are the potential dangers of high current in wires?

High current in wires can cause overheating, which can lead to electrical fires or damage to equipment. It can also pose a safety hazard to individuals if they come into contact with the current. It is important to properly regulate and control the current of wires to prevent these dangers.

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