Ampere's Circuital Equation Calculator

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✖Magnetic Field Strength, denoted by the symbol H, is a measure of the intensity of a magnetic field within a material or a region of space.ⓘ Magnetic Field Strength [H_o]			+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%

✖Amperes Circuital Current (I) refers specifically to the total enclosed current that threads through a closed loop.ⓘ Ampere's Circuital Equation [I]

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Formula

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Ampere's Circuital Equation

Formula

`"I" = int("H"_{"o"}*x,x,0,"L")`

Example

`"0.036A"=int("1.8A/m"*x,x,0,"0.2m")`

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Ampere's Circuital Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Amperes Circuital Current = int(Magnetic Field Strength*x,x,0,Integral Path Length)
I = int(H_o*x,x,0,L)
This formula uses 1 Functions, 3 Variables

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

Amperes Circuital Current - (Measured in Ampere) - Amperes Circuital Current (I) refers specifically to the total enclosed current that threads through a closed loop.
Magnetic Field Strength - (Measured in Ampere per Meter) - Magnetic Field Strength, denoted by the symbol H, is a measure of the intensity of a magnetic field within a material or a region of space.
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

Magnetic Field Strength: 1.8 Ampere per Meter --> 1.8 Ampere per Meter No Conversion Required
Integral Path Length: 0.2 Meter --> 0.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = int(H_o*x,x,0,L) --> int(1.8*x,x,0,0.2)

Evaluating ... ...

I = 0.036

STEP 3: Convert Result to Output's Unit

0.036 Ampere --> No Conversion Required

FINAL ANSWER

0.036 Ampere <-- Amperes Circuital Current

(Calculation completed in 00.020 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

Ampere's Circuital Equation Formula

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

What are the Applications of Ampere's Circuital Equation ?

Calculating Magnetic Field of Simple Geometries:
1.Long, straight wires: Helps determine the magnetic field strength at a specific distance from a current-carrying wire.

2.Solenoids: Predicts the nearly uniform and strong magnetic field inside a long solenoid with many turns.

3.Toroids: Calculates the magnetic field within a toroid (donut-shaped coil), which is useful in transformers.

How to Calculate Ampere's Circuital Equation?

Ampere's Circuital Equation calculator uses Amperes Circuital Current = int(Magnetic Field Strength*x,x,0,Integral Path Length) to calculate the Amperes Circuital Current, The Ampere's Circuital Equation states that the line integral of H about any closed path is exactly equal to the direct current enclosed by that path. Amperes Circuital Current is denoted by I symbol.

How to calculate Ampere's Circuital Equation using this online calculator? To use this online calculator for Ampere's Circuital Equation, enter Magnetic Field Strength (H_o) & Integral Path Length (L) and hit the calculate button. Here is how the Ampere's Circuital Equation calculation can be explained with given input values -> 0.036 = int(1.8*x,x,0,0.2).

FAQ

What is Ampere's Circuital Equation?

The Ampere's Circuital Equation states that the line integral of H about any closed path is exactly equal to the direct current enclosed by that path and is represented as I = int(H_o*x,x,0,L) or Amperes Circuital Current = int(Magnetic Field Strength*x,x,0,Integral Path Length). Magnetic Field Strength, denoted by the symbol H, is a measure of the intensity of a magnetic field within a material or a region of space & 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 Ampere's Circuital Equation?

The Ampere's Circuital Equation states that the line integral of H about any closed path is exactly equal to the direct current enclosed by that path is calculated using Amperes Circuital Current = int(Magnetic Field Strength*x,x,0,Integral Path Length). To calculate Ampere's Circuital Equation, you need Magnetic Field Strength (H_o) & Integral Path Length (L). With our tool, you need to enter the respective value for Magnetic Field Strength & Integral Path 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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