Maximum distance of charge from current carrying wire

In summary, The conversation discusses two different ways of solving a problem involving a charged particle at a distance x with velocity v away from a current carrying wire with current I. The first method involves finding forces in the x and y-axis and solving differential equations, while the second method involves integrating the deviation of the charged particle over strips of magnetic field. However, there is a discrepancy in the results of the second method, and it is suggested that there may be a mistake in the integration process. The request is made for the second method to be shared with details and steps.
  • #1
Algren
74
1
Lets have a charged particle at a distance x at the beginning with velocity v away from a current carrying wire with current I. So, what will be the maximum distance of the particle from the wire? (only consider magnetic field)(wire is of infinite length)

There are two ways of solving the problem.

One is: Find forces in x and y-axis at a given time, get diff. equations, and solve em, and integrate tem.

Another is: We consider strips of magnetic field with 'dx' thickness, and integrate the deviation 'dθ' of the charged particle over all these strips from 0 to ∏/2. But in this case, i end up integrating sin(dθ). If i integrate sin(θ) dθ instead, i get the correct answer as so derived from the first way.

But i wanted to ask, is there any problem with the logic of the second way?
 
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  • #2
Algren said:
Another is: We consider strips of magnetic field with 'dx' thickness, and integrate the deviation 'dθ' of the charged particle over all these strips from 0 to ∏/2. But in this case, i end up integrating sin(dθ). If i integrate sin(θ) dθ instead, i get the correct answer as so derived from the first way.

But i wanted to ask, is there any problem with the logic of the second way?

How do you end up with integrating sin(dθ) ? You should be integrating sinθ w.r.t θ. Show me your work. You should have done any careless or conceptual mistake. Otherwise you shouldn't have arrived at such strange result.

Please post your second method here (with details and steps inclusive).
 

What is the maximum distance of charge from a current carrying wire?

The maximum distance of charge from a current carrying wire is dependent on several factors such as the magnitude of the current, the type of wire, and the surrounding environment. In general, the maximum distance is around 1.5 meters, but this can vary significantly.

How does the magnitude of the current affect the maximum distance of charge?

The greater the magnitude of the current, the stronger the magnetic field around the wire. This magnetic field can attract or repel charges, causing them to move closer or farther away from the wire. As a result, a higher current can lead to a larger maximum distance of charge from the wire.

Does the type of wire used impact the maximum distance of charge?

Yes, the type of wire used can affect the maximum distance of charge from the current carrying wire. Different materials have different conductivities, resistivities, and magnetic properties, all of which can influence the strength and shape of the magnetic field around the wire.

How does the surrounding environment affect the maximum distance of charge?

The surrounding environment can have an impact on the maximum distance of charge from a current carrying wire. For example, if there are other nearby sources of magnetic fields, they can interact and affect the shape and strength of the magnetic field around the wire, potentially altering the maximum distance of charge.

Is there a specific equation or formula for calculating the maximum distance of charge from a current carrying wire?

There is no single equation or formula for calculating the maximum distance of charge from a current carrying wire. It is a complex phenomenon that is affected by multiple factors, and the calculation would require knowledge of the wire properties, the current magnitude, and the surrounding environment. It is usually calculated through experiments and simulations rather than a simple equation.

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