Voltage of a point around an infinite long charged wire.

In summary, the question asks how to determine the voltage at a point p given an infinitely long wire with charge per length λ and the wire extending infinitely parallel to the X-Axis. One method is to use the expression dV = κ(λ dx)/√(x2 + y2) and integrate from -∞ to +∞, but this does not converge. Khan Academy has a worked example that may provide a solution.
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Lets say i have a infinitely long wire with charge per length, λ and a point, p of a position with its closest distance to the wire is y. The wire extend infinitely parallel to X-Axis. How to determine the voltage at the position p?

Can i first regard the voltage contributed by a very small charge in this expression:

dV = κ(λ dx)/√(x2 + y2) ...where κ = 1/4Ωε

v = κ(λ) ∫ dx/√(x2 + y2)
= κλ ln( √(x2 + y2 + x)

If the integral start from -∞ to +∞ of x, the formula does not converge, but my logic tells me that the charge of the wire at infinity doesn't affect the voltage at point p. Does this mean my approach is wrong?
 
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FAQ: Voltage of a point around an infinite long charged wire.

What is the concept of voltage?

Voltage is the measure of electric potential difference between two points in an electric field. It is the amount of potential energy per unit charge that is required to move a charge from one point to another.

How is voltage related to an infinite long charged wire?

An infinite long charged wire creates an electric field around it, which is characterized by a voltage. The electric field is strongest close to the wire and decreases as the distance from the wire increases. This results in a change in voltage at different points around the wire.

How is voltage calculated for a point around an infinite long charged wire?

The voltage at a point around an infinite long charged wire can be calculated using the formula V = kλ/2πε0ln(r/r0), where V is the voltage, k is Coulomb's constant, λ is the charge per unit length of the wire, ε0 is the permittivity of free space, r is the distance from the wire, and r0 is a reference distance.

How does the voltage change as the distance from the wire increases?

As the distance from the wire increases, the voltage decreases. This is because the electric field created by the wire becomes weaker as the distance increases, resulting in a lower potential energy per unit charge required to move a charge from one point to another.

Can the voltage around an infinite long charged wire be negative?

Yes, the voltage around an infinite long charged wire can be negative. This occurs when the reference distance, r0, is chosen to be inside the wire rather than outside. In this case, the voltage decreases as the distance from the wire increases, resulting in a negative value.

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