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

Credits

Created by Vignesh Naidu
Vellore Institute of Technology (VIT), Vellore,Tamil Nadu
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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)
Ar = 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 Ar 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 Ar = 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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