Retarded Vector Magnetic Potential Calculator

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✖Magnetic Permeability of Medium is the measure of magnetization that a material obtains in response to an applied magnetic field.ⓘ Magnetic Permeability of Medium [μ]			+10% -10%
✖Amperes Circuital Current (I) refers specifically to the total enclosed current that threads through a closed loop.ⓘ Amperes Circuital Current [I]			+10% -10%
✖Perpendicular Distance is the distance from the current element dl to the point where you're calculating the magnetic field.ⓘ Perpendicular Distance [r]			+10% -10%
✖Length is the measurement or extent of something from end to end.ⓘ Length [L]			+10% -10%

✖Retarded Vector Magnetic Potential relates to the magnetic vector potential in the context of the retarded potentials, which account for the finite speed of light with units of tesla-meters.ⓘ Retarded Vector Magnetic Potential [A_r]

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Formula

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Retarded Vector Magnetic Potential

Formula

`"A"_{"r"} = int(("μ"*"I"*x)/(4*pi*"r"),x,0,"L")`

Example

`"0.008317"=int(("0.02H/m"*"0.036A"*x)/(4*pi*"0.031"),x,0,"3m")`

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Retarded Vector Magnetic Potential Solution

STEP 0: Pre-Calculation Summary

Formula Used

Retarded Vector Magnetic Potential = int((Magnetic Permeability of Medium*Amperes Circuital Current*x)/(4*pi*Perpendicular Distance),x,0,Length)
A_r = int((μ*I*x)/(4*pi*r),x,0,L)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Retarded Vector Magnetic Potential - Retarded Vector Magnetic Potential relates to the magnetic vector potential in the context of the retarded potentials, which account for the finite speed of light with units of tesla-meters.
Magnetic Permeability of Medium - (Measured in Henry per Meter) - Magnetic Permeability of Medium is the measure of magnetization that a material obtains in response to an applied magnetic field.
Amperes Circuital Current - (Measured in Ampere) - Amperes Circuital Current (I) refers specifically to the total enclosed current that threads through a closed loop.
Perpendicular Distance - Perpendicular Distance is the distance from the current element dl to the point where you're calculating the magnetic field.
Length - (Measured in Meter) - Length is the measurement or extent of something from end to end.

STEP 1: Convert Input(s) to Base Unit

Magnetic Permeability of Medium: 0.02 Henry per Meter --> 0.02 Henry per Meter No Conversion Required
Amperes Circuital Current: 0.036 Ampere --> 0.036 Ampere No Conversion Required
Perpendicular Distance: 0.031 --> No Conversion Required
Length: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_r = int((μ*I*x)/(4*pi*r),x,0,L) --> int((0.02*0.036*x)/(4*pi*0.031),x,0,3)

Evaluating ... ...

A_r = 0.00831712928415711

STEP 3: Convert Result to Output's Unit

0.00831712928415711 --> No Conversion Required

FINAL ANSWER

0.00831712928415711 ≈ 0.008317 <-- Retarded Vector Magnetic Potential

(Calculation completed in 00.004 seconds)

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Created by Vignesh Naidu

Vellore Institute of Technology (VIT), Vellore,Tamil Nadu

Vignesh Naidu has created this Calculator and 25+ more calculators!

Verified by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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< 20 Magnetic Forces and Materials Calculators

Biot-Savart Equation

Go Magnetic Field Strength = int(Electric Current*x*sin(Theta)/(4*pi*(Perpendicular Distance^2)),x,0,Integral Path Length)

Retarded Vector Magnetic Potential

Go Retarded Vector Magnetic Potential = int((Magnetic Permeability of Medium*Amperes Circuital Current*x)/(4*pi*Perpendicular Distance),x,0,Length)

Biot-Savart Equation using Current Density

Go Magnetic Field Strength = int(Current Density*x*sin(Theta)/(4*pi*(Perpendicular Distance)^2),x,0,Volume)

Vector Magnetic Potential

Go Vector Magnetic Potential = int(([Permeability-vacuum]*Electric Current*x)/(4*pi*Perpendicular Distance),x,0,Integral Path Length)

Vector Magnetic Potential using Current Density

Go Vector Magnetic Potential = int(([Permeability-vacuum]*Current Density*x)/(4*pi*Perpendicular Distance),x,0,Volume)

Magnetic Force by Lorentz Force Equation

Go Magnetic force = Charge of Particle*(Electric Field+(Speed of Charged Particle*Magnetic Flux Density*sin(Theta)))

Electric Potential in Magnetic Field

Go Electric Potential = int((Volume Charge Density*x)/(4*pi*Permittivity*Perpendicular Distance),x,0,Volume)

Resistance of Cylindrical Conductor

Go Resistance of Cylindrical Conductor = Length of Cylindrical Conductor/(Electrical Conductivity*Cross Sectional Area of Cylindrical)

Magnetic Scalar Potential

Go Magnetic Scalar Potential = -(int(Magnetic Field Strength*x,x,Upper Limit,Lower Limit))

Current Flowing through N-Turn Coil

Go Electric Current = (int(Magnetic Field Strength*x,x,0,Length))/Number of Turns of Coil

Magnetization using Magnetic Field Strength, and Magnetic Flux Density

Go Magnetization = (Magnetic Flux Density/[Permeability-vacuum])-Magnetic Field Strength

Magnetic Flux Density using Magnetic Field Strength, and Magnetization

Go Magnetic Flux Density = [Permeability-vacuum]*(Magnetic Field Strength+Magnetization)

Ampere's Circuital Equation

Go Amperes Circuital Current = int(Magnetic Field Strength*x,x,0,Integral Path Length)

Absolute Permeability using Relative Permeability and Permeability of Free Space

Go Absolute Permeability of Material = Relative Permeability of Material*[Permeability-vacuum]

Electromotive Force about Closed Path

Go Electromotive Force = int(Electric Field*x,x,0,Length)

Free Space Magnetic Flux Density

Go Free space Magnetic Flux Density = [Permeability-vacuum]*Magnetic Field Strength

Net Bound Current

Go Net Bound Current = int(Magnetization,x,0,Length)

Internal Inductance of Long Straight Wire

Go Internal Inductance of Long Straight Wire = Magnetic Permeability/(8*pi)

Magnetomotive Force given Reluctance and Magnetic Flux

Go Magnetomotive Voltage = Magnetic Flux*Reluctance

Magnetic Susceptibility using relative permeability

Go Magnetic Susceptibility = Magnetic Permeability-1

Retarded Vector Magnetic Potential Formula

Retarded Vector Magnetic Potential = int((Magnetic Permeability of Medium*Amperes Circuital Current*x)/(4*pi*Perpendicular Distance),x,0,Length)
A_r = int((μ*I*x)/(4*pi*r),x,0,L)

What are the Applications of Retarded Vector Magnetic Potential ?

1. Antenna Theory and Radiation: Understanding how electromagnetic waves propagate from antennas requires considering the retarded potentials for both electric and magnetic fields.
2. Wireless Communication: Analyzing the behavior of electromagnetic waves in wireless communication systems relies heavily on the concept of retarded potentials.
3. Electrodynamics of Moving Charges: When dealing with accelerating charges and their associated electromagnetic fields, retarded potentials are essential for accurate calculations.

How to Calculate Retarded Vector Magnetic Potential?

Retarded Vector Magnetic Potential calculator uses Retarded Vector Magnetic Potential = int((Magnetic Permeability of Medium*Amperes Circuital Current*x)/(4*pi*Perpendicular Distance),x,0,Length) to calculate the Retarded Vector Magnetic Potential, The Retarded Vector Magnetic Potential formula calculates the magnetic vector potential at a point due to a current distribution, considering the magnetic permeability of the material and current flowing which is a function of retarded time. Retarded Vector Magnetic Potential is denoted by A_r symbol.

How to calculate Retarded Vector Magnetic Potential using this online calculator? To use this online calculator for Retarded Vector Magnetic Potential, enter Magnetic Permeability of Medium (μ), Amperes Circuital Current (I), Perpendicular Distance (r) & Length (L) and hit the calculate button. Here is how the Retarded Vector Magnetic Potential calculation can be explained with given input values -> 0.008317 = int((0.02*0.036*x)/(4*pi*0.031),x,0,3).

FAQ

What is Retarded Vector Magnetic Potential?

The Retarded Vector Magnetic Potential formula calculates the magnetic vector potential at a point due to a current distribution, considering the magnetic permeability of the material and current flowing which is a function of retarded time and is represented as A_r = int((μ*I*x)/(4*pi*r),x,0,L) or Retarded Vector Magnetic Potential = int((Magnetic Permeability of Medium*Amperes Circuital Current*x)/(4*pi*Perpendicular Distance),x,0,Length). Magnetic Permeability of Medium is the measure of magnetization that a material obtains in response to an applied magnetic field, Amperes Circuital Current (I) refers specifically to the total enclosed current that threads through a closed loop, Perpendicular Distance is the distance from the current element dl to the point where you're calculating the magnetic field & Length is the measurement or extent of something from end to end.

How to calculate Retarded Vector Magnetic Potential?

The Retarded Vector Magnetic Potential formula calculates the magnetic vector potential at a point due to a current distribution, considering the magnetic permeability of the material and current flowing which is a function of retarded time is calculated using Retarded Vector Magnetic Potential = int((Magnetic Permeability of Medium*Amperes Circuital Current*x)/(4*pi*Perpendicular Distance),x,0,Length). To calculate Retarded Vector Magnetic Potential, you need Magnetic Permeability of Medium (μ), Amperes Circuital Current (I), Perpendicular Distance (r) & Length (L). With our tool, you need to enter the respective value for Magnetic Permeability of Medium, Amperes Circuital Current, Perpendicular Distance & Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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