Magnetic Field at Center of Arc Calculator

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✖Electric Current is the time rate of flow of charge through a cross sectional area.ⓘ Electric Current [i]			+10% -10%
✖Angle Obtained by Arc at Center is the angle made by the arc at the centre in radians.ⓘ Angle Obtained by Arc at Center [θ]			+10% -10%
✖Radius of Ring is a line segment extending from the center of a circle or sphere to the circumference or bounding surface.ⓘ Radius of Ring [r_ring]			+10% -10%

✖Field at Center of Arc is the magnetic field which generated by flowing current through circular arc.ⓘ Magnetic Field at Center of Arc [M_arc]

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Formula

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Magnetic Field at Center of Arc

Formula

`"M"_{"arc"} = ("[Permeability-vacuum]"*"i"*"θ")/(4*pi*"r"_{"ring"})`

Example

`"3.2E^-7Wb/m²"=("[Permeability-vacuum]"*"2.2A"*"0.5°")/(4*pi*"6mm")`

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Download Magnetic Field due to Current Formulas PDF

Magnetic Field at Center of Arc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring)
M_arc = ([Permeability-vacuum]*i*θ)/(4*pi*r_ring)
This formula uses 2 Constants, 4 Variables

Constants Used

[Permeability-vacuum] - Permeability of vacuum Value Taken As 1.2566E-6
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Field at Center of Arc - (Measured in Tesla) - Field at Center of Arc is the magnetic field which generated by flowing current through circular arc.
Electric Current - (Measured in Ampere) - Electric Current is the time rate of flow of charge through a cross sectional area.
Angle Obtained by Arc at Center - (Measured in Radian) - Angle Obtained by Arc at Center is the angle made by the arc at the centre in radians.
Radius of Ring - (Measured in Meter) - Radius of Ring is a line segment extending from the center of a circle or sphere to the circumference or bounding surface.

STEP 1: Convert Input(s) to Base Unit

Electric Current: 2.2 Ampere --> 2.2 Ampere No Conversion Required
Angle Obtained by Arc at Center: 0.5 Degree --> 0.00872664625997001 Radian (Check conversion here)
Radius of Ring: 6 Millimeter --> 0.006 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_arc = ([Permeability-vacuum]*i*θ)/(4*pi*r_ring) --> ([Permeability-vacuum]*2.2*0.00872664625997001)/(4*pi*0.006)

Evaluating ... ...

M_arc = 3.19977029532234E-07

STEP 3: Convert Result to Output's Unit

3.19977029532234E-07 Tesla -->3.19977029532234E-07 Weber per Square Meter (Check conversion here)

FINAL ANSWER

3.19977029532234E-07 ≈ 3.2E-7 Weber per Square Meter <-- Field at Center of Arc

(Calculation completed in 00.004 seconds)

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Credits

Created by Aditya Ranjan

Indian Institute of Technology (IIT), Mumbai

Aditya Ranjan has created this Calculator and 6 more calculators!

Verified by Pragati Jaju

College Of Engineering (COEP), Pune

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< 15 Magnetic Field due to Current Calculators

Magnetic Field due to Straight Conductor

Go Magnetic Field = ([Permeability-vacuum]*Electric Current)/(4*pi*Perpendicular Distance)*(cos(Theta 1)-cos(Theta 2))

Magnetic Field for Tangent Galvanometer

Go Horizontal Component of Earth's Magnetic Field = ([Permeability-vacuum]*Number of Turns of Coil*Electric Current)/(2*Radius of Ring*tan(Angle of Deflection of Galvanometer))

Force between Parallel Wires

Go Magnetic Force per Unit Length = ([Permeability-vacuum]*Electric Current in Conductor 1*Electric Current in Conductor 2)/(2*pi*Perpendicular Distance)

Current in Moving Coil Galvanometer

Go Electric Current = (Spring Constant*Angle of Deflection of Galvanometer)/(Number of Turns of Coil*Cross-Sectional Area*Magnetic Field)

Magnetic Field on Axis of Ring

Go Magnetic Field = ([Permeability-vacuum]*Electric Current*Radius of Ring^2)/(2*(Radius of Ring^2+Perpendicular Distance^2)^(3/2))

Time Period of Magnetometer

Go Time Period of Magnetometer = 2*pi*sqrt(Moment of Inertia/(Magnetic Moment*Horizontal Component of Earth's Magnetic Field))

Magnetic Field at Center of Arc

Go Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring)

Field of Bar Magnet at Equatorial position

Go Field at Equitorial Position of Bar Magnet = ([Permeability-vacuum]*Magnetic Moment)/(4*pi*Distance from Center to Point^3)

Field of Bar Magnet at Axial position

Go Field at Axial Position of Bar Magnet = (2*[Permeability-vacuum]*Magnetic Moment)/(4*pi*Distance from Center to Point^3)

Field Inside Solenoid

Go Magnetic Field = ([Permeability-vacuum]*Electric Current*Number of Turns)/Length of Solonoid

Magnetic Field Due to Infinite Straight Wire

Go Magnetic Field = ([Permeability-vacuum]*Electric Current)/(2*pi*Perpendicular Distance)

Electric Current for Tangent Galvanometer

Go Electric Current = Reduction Factor of Tangent Galvanometer*tan(Angle of Deflection of Galvanometer)

Angle of Dip

Go Angle of Dip = arccos(Horizontal Component of Earth's Magnetic Field/Net Earth's Magnetic Field)

Magnetic Field at Center of Ring

Go Field at Center of Ring = ([Permeability-vacuum]*Electric Current)/(2*Radius of Ring)

Magnetic Permeability

Go Magnetic Permeability of Medium = Magnetic Field/Magnetic Field Intensity

Magnetic Field at Center of Arc Formula

Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring)
M_arc = ([Permeability-vacuum]*i*θ)/(4*pi*r_ring)

What is the magnetic field at the center of an arc of current of radius R?

The arc curves through an angle θ. If the current is counter-clockwise the magnetic field at the center is out of the page.

The magnetic field dB from a representative piece of the wire is:
dB = μo I dl /4π r^2

Our integral for the net field is easy:
B =μo I/4π R2 ∫ dl
B = μo I s/4π R2

where s is the arc length, equal to Rθ.
Therefore B =μo I θ/4π R

How to Calculate Magnetic Field at Center of Arc?

Magnetic Field at Center of Arc calculator uses Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring) to calculate the Field at Center of Arc, The Magnetic Field at Center of Arc is the magnetic field generated by the arc of wire at the centre due to the flow of current through the wire. Field at Center of Arc is denoted by M_arc symbol.

How to calculate Magnetic Field at Center of Arc using this online calculator? To use this online calculator for Magnetic Field at Center of Arc, enter Electric Current (i), Angle Obtained by Arc at Center (θ) & Radius of Ring (r_ring) and hit the calculate button. Here is how the Magnetic Field at Center of Arc calculation can be explained with given input values -> 3.2E-7 = ([Permeability-vacuum]*2.2*0.00872664625997001)/(4*pi*0.006).

FAQ

What is Magnetic Field at Center of Arc?

The Magnetic Field at Center of Arc is the magnetic field generated by the arc of wire at the centre due to the flow of current through the wire and is represented as M_arc = ([Permeability-vacuum]*i*θ)/(4*pi*r_ring) or Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring). Electric Current is the time rate of flow of charge through a cross sectional area, Angle Obtained by Arc at Center is the angle made by the arc at the centre in radians & Radius of Ring is a line segment extending from the center of a circle or sphere to the circumference or bounding surface.

How to calculate Magnetic Field at Center of Arc?

The Magnetic Field at Center of Arc is the magnetic field generated by the arc of wire at the centre due to the flow of current through the wire is calculated using Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring). To calculate Magnetic Field at Center of Arc, you need Electric Current (i), Angle Obtained by Arc at Center (θ) & Radius of Ring (r_ring). With our tool, you need to enter the respective value for Electric Current, Angle Obtained by Arc at Center & Radius of Ring 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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