Vector Magnetic Potential using Current Density Calculator

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✖Current Density describes how much current is flowing through a unit area of a conductor. It essentially tells you the concentration of current within the material.ⓘ Current Density [J]			+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%
✖Volume is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume [V_T]			+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 using Current Density [A]

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Formula

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Vector Magnetic Potential using Current Density

Formula

`"A" = int(("[Permeability-vacuum]"*"J"*x)/(4*pi*"r"),x,0,"V"_{"T"})`

Example

`"1.4E^-7"=int(("[Permeability-vacuum]"*"0.2199A/m²"*x)/(4*pi*"0.031"),x,0,"0.63m³")`

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Vector Magnetic Potential using Current Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vector Magnetic Potential = int(([Permeability-vacuum]*Current Density*x)/(4*pi*Perpendicular Distance),x,0,Volume)
A = int(([Permeability-vacuum]*J*x)/(4*pi*r),x,0,V_T)
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)).
Current Density - (Measured in Ampere per Square Meter) - Current Density describes how much current is flowing through a unit area of a conductor. It essentially tells you the concentration of current within the material.
Perpendicular Distance - Perpendicular Distance is the distance from the current element dl to the point where you're calculating the magnetic field.
Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies or that is enclosed within a container.

STEP 1: Convert Input(s) to Base Unit

Current Density: 0.2199 Ampere per Square Meter --> 0.2199 Ampere per Square Meter No Conversion Required
Perpendicular Distance: 0.031 --> No Conversion Required
Volume: 0.63 Cubic Meter --> 0.63 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = int(([Permeability-vacuum]*J*x)/(4*pi*r),x,0,V_T) --> int(([Permeability-vacuum]*0.2199*x)/(4*pi*0.031),x,0,0.63)

Evaluating ... ...

A = 1.40771467741935E-07

STEP 3: Convert Result to Output's Unit

1.40771467741935E-07 --> No Conversion Required

FINAL ANSWER

1.40771467741935E-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 using Current Density Formula

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

What is the Application of Vector Magnetic Potential given Current Density ?

Electromagnetic Waves and Antennas: The vector potential plays a crucial role in describing electromagnetic waves and how antennas function. It helps analyze the electric and magnetic fields produced by antennas, which is essential for designing and understanding wireless communication systems.

How to Calculate Vector Magnetic Potential using Current Density?

Vector Magnetic Potential using Current Density calculator uses Vector Magnetic Potential = int(([Permeability-vacuum]*Current Density*x)/(4*pi*Perpendicular Distance),x,0,Volume) to calculate the Vector Magnetic Potential, The Vector Magnetic Potential using Current Density formula is a specific integral formula that allows you to calculate A, essentially relating the magnetic properties of a space to the way current flows within it. Vector Magnetic Potential is denoted by A symbol.

How to calculate Vector Magnetic Potential using Current Density using this online calculator? To use this online calculator for Vector Magnetic Potential using Current Density, enter Current Density (J), Perpendicular Distance (r) & Volume (V_T) and hit the calculate button. Here is how the Vector Magnetic Potential using Current Density calculation can be explained with given input values -> 4.5E-8 = int(([Permeability-vacuum]*0.2199*x)/(4*pi*0.031),x,0,0.63).

FAQ

What is Vector Magnetic Potential using Current Density?

The Vector Magnetic Potential using Current Density formula is a specific integral formula that allows you to calculate A, essentially relating the magnetic properties of a space to the way current flows within it and is represented as A = int(([Permeability-vacuum]*J*x)/(4*pi*r),x,0,V_T) or Vector Magnetic Potential = int(([Permeability-vacuum]*Current Density*x)/(4*pi*Perpendicular Distance),x,0,Volume). Current Density describes how much current is flowing through a unit area of a conductor. It essentially tells you the concentration of current within the material, Perpendicular Distance is the distance from the current element dl to the point where you're calculating the magnetic field & Volume is the amount of space that a substance or object occupies or that is enclosed within a container.

How to calculate Vector Magnetic Potential using Current Density?

The Vector Magnetic Potential using Current Density formula is a specific integral formula that allows you to calculate A, essentially relating the magnetic properties of a space to the way current flows within it is calculated using Vector Magnetic Potential = int(([Permeability-vacuum]*Current Density*x)/(4*pi*Perpendicular Distance),x,0,Volume). To calculate Vector Magnetic Potential using Current Density, you need Current Density (J), Perpendicular Distance (r) & Volume (V_T). With our tool, you need to enter the respective value for Current Density, Perpendicular Distance & Volume 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 Current Density, Perpendicular Distance & Volume. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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