Electric Field for Line of Charge

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on

Sep 29, 2022, 12:52:23 AM

Created by

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Jan 26, 2017, 3:44:26 AM

E = \frac{2 \cdot k \cdot λ}{r} = \frac{2 \cdot k \cdot (\frac{C}{l})}{r}

$E = (2*k*lambda)/ "r" = (2*k*(C/l) )/ "r"$

(C) Charge

$(C)"Charge"$

(l) unit length

$(l)"unit length"$

(r) Distance from Line

$(r)"Distance from Line"$

The Math / Science

The Electric Field for Line of Charge equation assumes a long line of point charges, each a minute charge element. The individual electric fields of each of these point charges are imagined as overlapping fields and thus the composite electric field of all the point charges lined up generates the electric field we compute here at any radial distance from the line of charges. The resultant electric field we calculate here is typically represented in standard units of V/m. In vCalc, of course, the calculated electric field can be computed in numerous different units of elect field intensity.

The Electric Field for Line of Charge equation is as follows:

$E = 2 \cdot k \cdot \frac{λ}{r}$ $E=2*k*lambda/r$

where

$E$ $E$ is the electric field
$k$ $k$ is the constant: $\frac{1}{4 \cdot π \cdot ε_{0}}$ $1/(4*pi*epsilon_0)$
$λ$ $lambda$ is the charge per unit length
$r$ $r$ is the distance from the line charge

Because $λ$ $lambda$ is a charge per unit length, we substitute $\frac{C}{l}$ $C/l$ for $λ$ $lambda$ , making $C$ $C$ and $l$ $l$ inputs to the equation

where

$C$ $C$ is the electric charge (typically in Coulombs, but you can choose your own units)
$l$ $l$ is the unit length (typically in meters, but again you can choose your own units.

Notes on using this vCalc equation

Note 1: To have $λ$ $lambda$ work properly as units of charge per unit length, you can change the units of $l$ $l$ but leave the value of $l$ $l$ as 1.

Note 2: ε₀ is the Permittivityof a vacuum and is approximately to 8.854187817E-12 F/m. We use the vCalc constant for the Permittivityof a vacuum.

Inputs

$C$ $C$ is the electric charge
$l$ $l$ is the unit length
$r$ $r$ is the distance from the line charge

Units of electric field intensity

Units of electric field intensity offered in vCalc are: $\frac{V}{m} = \frac{N}{C} = \frac{k g f}{C} = \frac{l b f}{C} = \frac{V}{ft} = \frac{V}{in}$ $V/m = N/C = (kgf)/C = (lbf)/C = V/"ft" = V/"in"$

Electric Field for Line of Charge

The Math / Science

Notes on using this vCalc equation

Inputs

Units of electric field intensity

See also

Datasets

Equations and Data Items

Calculators

Equations and Data Items

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