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Field at Center of an arc Solution

STEP 0: Pre-Calculation Summary
Formula Used
Field at the Center of an arc = [Permeability-vacuum]*Electric Current*Angle obtained by an Arc at Center/(4*pi*Radius)
M = [Permeability-vacuum]*i*theta/(4*pi*r)
This formula uses 2 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
Electric Current - Electric Current is the time rate of flow of charge through a cross sectional area. (Measured in Ampere)
Angle obtained by an Arc at Center - Angle obtained by an Arc at Center is the angle made by the arc at the centre in radians. (Measured in Radian)
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Electric Current: 1 Ampere --> 1 Ampere No Conversion Required
Angle obtained by an Arc at Center: 0.5 Radian --> 0.5 Radian No Conversion Required
Radius: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
M = [Permeability-vacuum]*i*theta/(4*pi*r) --> [Permeability-vacuum]*1*0.5/(4*pi*10)
Evaluating ... ...
M = 5E-09
STEP 3: Convert Result to Output's Unit
5E-09 Tesla -->5E-09 Weber per Square Metre (Check conversion here)
FINAL ANSWER
5E-09 Weber per Square Metre <-- Field at the Center of an arc
(Calculation completed in 00.015 seconds)

10+ Magnetic Field Due to Current Calculators

Magnetic Field for Tangent Galvanometer
Horizontal Component of Earth's Magnetic Field = ([Permeability-vacuum]*Number of Turns of a coil*Electric Current)/(2*Radius*tan(Angle of Deflection of galvanometer)) Go
Force Between Parallel Wires
Magnetic force per unit length = ([Permeability-vacuum]*Electric Current in Conductor 1*Electric Current in Conductor 2)/(2*pi*Perpendicular Distance) Go
Field at Center of an arc
Field at the Center of an arc = [Permeability-vacuum]*Electric Current*Angle obtained by an Arc at Center/(4*pi*Radius) Go
Magnetic Field on Axis of Ring
Magnetic Field = ([Permeability-vacuum]*Electric Current*Radius^2)/(2*((Radius^2)+(Perpendicular Distance^2))^(3/2)) Go
Field of Bar Magnet at equatorial position
Field at the equitorial position of a bar magnet = [Permeability-vacuum]*Magnetic Moment/((4*pi*Distance from center to a point)^3) Go
Field of Bar Magnet at axial position
Field at the axial position of a bar magnet = [Permeability-vacuum]*2*Magnetic Moment/(4*pi*(Distance from center to a point)^3) Go
Field inside solenoid
Magnetic Field = [Permeability-vacuum]*Electric Current*Number of Turns/Length Go
Electric Current for Tangent Galvanometer
Electric Current = Reduction Factor of Tangent Galvanometer*tan(Angle of Deflection of galvanometer) Go
Angle of Dip
Angle of Dip = arccos(Horizontal Component of Earth's Magnetic Field/Net Earth's Magnetic Field) Go
Magnetic field at center of ring
Field at the center of the ring = ([Permeability-vacuum]*Electric Current)/(2*Radius of Ring) Go

Field at Center of an arc Formula

Field at the Center of an arc = [Permeability-vacuum]*Electric Current*Angle obtained by an Arc at Center/(4*pi*Radius)
M = [Permeability-vacuum]*i*theta/(4*pi*r)

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 Field at Center of an arc?

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

How to calculate Field at Center of an arc using this online calculator? To use this online calculator for Field at Center of an arc, enter Electric Current (i), Angle obtained by an Arc at Center (theta) & Radius (r) and hit the calculate button. Here is how the Field at Center of an arc calculation can be explained with given input values -> 5.000E-9 = [Permeability-vacuum]*1*0.5/(4*pi*10).

FAQ

What is Field at Center of an arc?
Field at Center of an arc is the magnetic field generated by the arc of wire at the center due to the flow of current through the wire and is represented as M = [Permeability-vacuum]*i*theta/(4*pi*r) or Field at the Center of an arc = [Permeability-vacuum]*Electric Current*Angle obtained by an Arc at Center/(4*pi*Radius). Electric Current is the time rate of flow of charge through a cross sectional area, Angle obtained by an Arc at Center is the angle made by the arc at the centre in radians & Radius is a radial line from the focus to any point of a curve.
How to calculate Field at Center of an arc?
Field at Center of an arc is the magnetic field generated by the arc of wire at the center due to the flow of current through the wire is calculated using Field at the Center of an arc = [Permeability-vacuum]*Electric Current*Angle obtained by an Arc at Center/(4*pi*Radius). To calculate Field at Center of an arc, you need Electric Current (i), Angle obtained by an Arc at Center (theta) & Radius (r). With our tool, you need to enter the respective value for Electric Current, Angle obtained by an Arc at Center & Radius 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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