Biot-Savart Equation using Current Density Calculator

↳

Electronics

Chemical Engineering

Civil

Electrical

Electronics and Instrumentation

Materials Science

Mechanical

Production Engineering

⤿

Magnetic Forces and Materials

Electromagnetic Radiation and Antennas

Guided Waves in Field Theory

✖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%
✖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%
✖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%

✖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 using Current Density [H_o]

⎘ Copy

👎

Formula

✖

Biot-Savart Equation using Current Density

Formula

`"H"_{"o"} = int("J"*x*sin("θ"_{"em"})/(4*pi*("r")^2),x,0,"V"_{"T"})`

Example

`"1.806812A/m"=int("0.2199A/m²"*x*sin("30°")/(4*pi*("0.031")^2),x,0,"0.63m³")`

Calculator

LaTeX

Reset

👍

Download Electronics Formula PDF PDF Image

Biot-Savart Equation using Current Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnetic Field Strength = int(Current Density*x*sin(Theta)/(4*pi*(Perpendicular Distance)^2),x,0,Volume)
H_o = int(J*x*sin(θ_em)/(4*pi*(r)^2),x,0,V_T)
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.
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.
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 - 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
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
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

H_o = int(J*x*sin(θ_em)/(4*pi*(r)^2),x,0,V_T) --> int(0.2199*x*sin(0.5235987755982)/(4*pi*(0.031)^2),x,0,0.63)

Evaluating ... ...

H_o = 1.80681249495406

STEP 3: Convert Result to Output's Unit

1.80681249495406 Ampere per Meter --> No Conversion Required

FINAL ANSWER

1.80681249495406 ≈ 1.806812 Ampere per Meter <-- Magnetic Field Strength

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Electronics » Electromagnetic Field Theory » Magnetic Forces and Materials » Biot-Savart Equation using Current Density

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 using Current Density Formula

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

What are the Applications of the Biot-Savart Law with Current Density ?

1. Magnetic Field of Simple Geometries:
It allows us to calculate the magnetic field around:
Long, straight wires: Determine the B-field strength at a specific distance from a current-carrying wire.
Solenoids: Predict the strong and nearly uniform magnetic field inside a long solenoid with many turns.

2. Complex Current Configurations:
Current loops (circular, rectangular, etc.)
Current sheets (infinite or finite)
Arbitrary current distributions (using numerical methods)

How to Calculate Biot-Savart Equation using Current Density?

Biot-Savart Equation using Current Density calculator uses Magnetic Field Strength = int(Current Density*x*sin(Theta)/(4*pi*(Perpendicular Distance)^2),x,0,Volume) to calculate the Magnetic Field Strength, The Biot-Savart Equation using Current Density formula states that H at a point is proportional to the line integral of the vector cross product of current density (J) and a small length element (dl) across all current-carrying segments, divided by the square of the distance (r) from the source element to the point. Magnetic Field Strength is denoted by H_o symbol.

How to calculate Biot-Savart Equation using Current Density using this online calculator? To use this online calculator for Biot-Savart Equation using Current Density, enter Current Density (J), Theta (θ_em), Perpendicular Distance (r) & Volume (V_T) and hit the calculate button. Here is how the Biot-Savart Equation using Current Density calculation can be explained with given input values -> 0.181164 = int(0.2199*x*sin(0.5235987755982)/(4*pi*(0.031)^2),x,0,0.63).

FAQ

What is Biot-Savart Equation using Current Density?

The Biot-Savart Equation using Current Density formula states that H at a point is proportional to the line integral of the vector cross product of current density (J) and a small length element (dl) across all current-carrying segments, divided by the square of the distance (r) from the source element to the point and is represented as H_o = int(J*x*sin(θ_em)/(4*pi*(r)^2),x,0,V_T) or Magnetic Field Strength = int(Current Density*x*sin(Theta)/(4*pi*(Perpendicular Distance)^2),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, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint, 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 Biot-Savart Equation using Current Density?

The Biot-Savart Equation using Current Density formula states that H at a point is proportional to the line integral of the vector cross product of current density (J) and a small length element (dl) across all current-carrying segments, divided by the square of the distance (r) from the source element to the point is calculated using Magnetic Field Strength = int(Current Density*x*sin(Theta)/(4*pi*(Perpendicular Distance)^2),x,0,Volume). To calculate Biot-Savart Equation using Current Density, you need Current Density (J), Theta (θ_em), Perpendicular Distance (r) & Volume (V_T). With our tool, you need to enter the respective value for Current Density, Theta, 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 Magnetic Field Strength?

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

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

Home

FREE PDFs

🔍 Search