Vector Magnetic Potential Calculator

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✖Electric Current is the time rate of flow of charge through a cross sectional area.ⓘ Electric Current [i_p]			+10% -10%
✖The perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both.ⓘ Perpendicular Distance [d]			+10% -10%
✖Integral Path Length representing the specific route taken to sum the magnetic field contributions and determine the total field at a point.ⓘ Integral Path Length [L]			+10% -10%

✖Vector Magnetic Potential is a mathematical tool in electromagnetism that relates to the magnetic field. Its curl is equal to the magnetic field (B = curl(A)).ⓘ Vector Magnetic Potential [A]

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Formula

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Vector Magnetic Potential

Formula

`"A" = int(("[Permeability-vacuum]"*"i"_{"p"}*x)/(4*pi*"d"),x,0,"L")`

Example

`"1.4E^-7"=int(("[Permeability-vacuum]"*"2.2A"*x)/(4*pi*"31mm"),x,0,"0.2m")`

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Vector Magnetic Potential Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vector Magnetic Potential = int(([Permeability-vacuum]*Electric Current*x)/(4*pi*Perpendicular Distance),x,0,Integral Path Length)
A = int(([Permeability-vacuum]*i_p*x)/(4*pi*d),x,0,L)
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[Permeability-vacuum] - Permeability of vacuum Value Taken As 1.2566E-6
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

Vector Magnetic Potential - Vector Magnetic Potential is a mathematical tool in electromagnetism that relates to the magnetic field. Its curl is equal to the magnetic field (B = curl(A)).
Electric Current - (Measured in Ampere) - Electric Current is the time rate of flow of charge through a cross sectional area.
Perpendicular Distance - (Measured in Meter) - The perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both.
Integral Path Length - (Measured in Meter) - Integral Path Length representing the specific route taken to sum the magnetic field contributions and determine the total field at a point.

STEP 1: Convert Input(s) to Base Unit

Electric Current: 2.2 Ampere --> 2.2 Ampere No Conversion Required
Perpendicular Distance: 31 Millimeter --> 0.031 Meter (Check conversion here)
Integral Path Length: 0.2 Meter --> 0.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = int(([Permeability-vacuum]*i_p*x)/(4*pi*d),x,0,L) --> int(([Permeability-vacuum]*2.2*x)/(4*pi*0.031),x,0,0.2)

Evaluating ... ...

A = 1.41935483870968E-07

STEP 3: Convert Result to Output's Unit

1.41935483870968E-07 --> No Conversion Required

FINAL ANSWER

1.41935483870968E-07 ≈ 1.4E-7 <-- 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

Vector Magnetic Potential Formula

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

What are the Applications of Vector Magnetic Potential ?

1. Solving Boundary Value Problems: In electromagnetism, we often deal with problems where the magnetic field needs to satisfy certain conditions at boundaries (like between different materials). The vector potential can be a powerful tool for solving these boundary value problems.

2. Antenna Theory: Understanding the behavior of antennas, which radiate or receive electromagnetic waves, relies heavily on the concept of the vector potential. A plays a key role in describing the electromagnetic fields generated by antennas.

How to Calculate Vector Magnetic Potential?

Vector Magnetic Potential calculator uses Vector Magnetic Potential = int(([Permeability-vacuum]*Electric Current*x)/(4*pi*Perpendicular Distance),x,0,Integral Path Length) to calculate the Vector Magnetic Potential, The Vector Magnetic Potential formula is defined as a mathematical tool in electromagnetism that relates to the magnetic field. Its curl is equal to the magnetic field (B = curl(A)). Vector Magnetic Potential is denoted by A symbol.

How to calculate Vector Magnetic Potential using this online calculator? To use this online calculator for Vector Magnetic Potential, enter Electric Current (i_p), Perpendicular Distance (d) & Integral Path Length (L) and hit the calculate button. Here is how the Vector Magnetic Potential calculation can be explained with given input values -> 1.4E-7 = int(([Permeability-vacuum]*2.2*x)/(4*pi*0.031),x,0,0.2).

FAQ

What is Vector Magnetic Potential?

The Vector Magnetic Potential formula is defined as a mathematical tool in electromagnetism that relates to the magnetic field. Its curl is equal to the magnetic field (B = curl(A)) and is represented as A = int(([Permeability-vacuum]*i_p*x)/(4*pi*d),x,0,L) or Vector Magnetic Potential = int(([Permeability-vacuum]*Electric Current*x)/(4*pi*Perpendicular Distance),x,0,Integral Path Length). Electric Current is the time rate of flow of charge through a cross sectional area, The perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both & Integral Path Length representing the specific route taken to sum the magnetic field contributions and determine the total field at a point.

How to calculate Vector Magnetic Potential?

The Vector Magnetic Potential formula is defined as a mathematical tool in electromagnetism that relates to the magnetic field. Its curl is equal to the magnetic field (B = curl(A)) is calculated using Vector Magnetic Potential = int(([Permeability-vacuum]*Electric Current*x)/(4*pi*Perpendicular Distance),x,0,Integral Path Length). To calculate Vector Magnetic Potential, you need Electric Current (i_p), Perpendicular Distance (d) & Integral Path Length (L). With our tool, you need to enter the respective value for Electric Current, Perpendicular Distance & Integral Path Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Vector Magnetic Potential?

In this formula, Vector Magnetic Potential uses Electric Current, Perpendicular Distance & Integral Path Length. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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