Biot-Savart Equation Calculator

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Magnetic Forces and Materials

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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%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ_em]			+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%

✖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.ⓘ Biot-Savart Equation [H_o]

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Biot-Savart Equation

Formula

`"H"_{"o"} = int("i"_{"p"}*x*sin("θ"_{"em"})/(4*pi*("d"^2)),x,0,"L")`

Example

`"1.821753A/m"=int("2.2A"*x*sin("30°")/(4*pi*(("31mm")^2)),x,0,"0.2m")`

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Biot-Savart Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnetic Field Strength = int(Electric Current*x*sin(Theta)/(4*pi*(Perpendicular Distance^2)),x,0,Integral Path Length)
H_o = int(i_p*x*sin(θ_em)/(4*pi*(d^2)),x,0,L)
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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

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.
Electric Current - (Measured in Ampere) - Electric Current is the time rate of flow of charge through a cross sectional area.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
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
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
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

H_o = int(i_p*x*sin(θ_em)/(4*pi*(d^2)),x,0,L) --> int(2.2*x*sin(0.5235987755982)/(4*pi*(0.031^2)),x,0,0.2)

Evaluating ... ...

H_o = 1.82175273050036

STEP 3: Convert Result to Output's Unit

1.82175273050036 Ampere per Meter --> No Conversion Required

FINAL ANSWER

1.82175273050036 ≈ 1.821753 Ampere per Meter <-- Magnetic Field Strength

(Calculation completed in 00.004 seconds)

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Credits

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

Dipanjona Mallick has verified this Calculator and 50+ more calculators!

< 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

Biot-Savart Equation Formula

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

What are the applications of Biot-Savart Equation ?

Magnetic Field Calculations: It allows engineers and scientists to calculate the magnetic field generated by various current configurations, such as straight wires, loops, and solenoids. This knowledge is crucial for designing electromagnets, transformers, and motors.
Understanding Electromagnetic Forces: The law helps explain the forces experienced by charged particles (electrons, protons) moving in a magnetic field. This understanding is vital in various fields, including particle accelerators and plasma physics.

How to Calculate Biot-Savart Equation?

Biot-Savart Equation calculator uses Magnetic Field Strength = int(Electric Current*x*sin(Theta)/(4*pi*(Perpendicular Distance^2)),x,0,Integral Path Length) to calculate the Magnetic Field Strength, The Biot-Savart Equation formula relates the magnetic field strength at a point to the integral of the product of current, a tiny current element's vector, and the distance vector to that point. It essentially describes how electric currents generate magnetic fields. Magnetic Field Strength is denoted by H_o symbol.

How to calculate Biot-Savart Equation using this online calculator? To use this online calculator for Biot-Savart Equation, enter Electric Current (i_p), Theta (θ_em), Perpendicular Distance (d) & Integral Path Length (L) and hit the calculate button. Here is how the Biot-Savart Equation calculation can be explained with given input values -> 9.222623 = int(2.2*x*sin(0.5235987755982)/(4*pi*(0.031^2)),x,0,0.2).

FAQ

What is Biot-Savart Equation?

The Biot-Savart Equation formula relates the magnetic field strength at a point to the integral of the product of current, a tiny current element's vector, and the distance vector to that point. It essentially describes how electric currents generate magnetic fields and is represented as H_o = int(i_p*x*sin(θ_em)/(4*pi*(d^2)),x,0,L) or Magnetic Field Strength = int(Electric Current*x*sin(Theta)/(4*pi*(Perpendicular Distance^2)),x,0,Integral Path Length). Electric Current is the time rate of flow of charge through a cross sectional area, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint, 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 Biot-Savart Equation?

The Biot-Savart Equation formula relates the magnetic field strength at a point to the integral of the product of current, a tiny current element's vector, and the distance vector to that point. It essentially describes how electric currents generate magnetic fields is calculated using Magnetic Field Strength = int(Electric Current*x*sin(Theta)/(4*pi*(Perpendicular Distance^2)),x,0,Integral Path Length). To calculate Biot-Savart Equation, you need Electric Current (i_p), Theta (θ_em), Perpendicular Distance (d) & Integral Path Length (L). With our tool, you need to enter the respective value for Electric Current, Theta, 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 Magnetic Field Strength?

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

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

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