Magnetic Field at Center of Ring Solution

STEP 0: Pre-Calculation Summary
Formula Used
Field at Center of Ring = ([Permeability-vacuum]*Electric Current)/(2*Radius of Ring)
Mring = ([Permeability-vacuum]*i)/(2*rring)
This formula uses 1 Constants, 3 Variables
Constants Used
[Permeability-vacuum] - Permeability of vacuum Value Taken As 1.2566E-6
Variables Used
Field at Center of Ring - (Measured in Tesla) - Field at center of ring is given by B=μ0I2R (at center of loop), where R is the radius of the loop. RHR-2 gives the direction of the field about the loop.
Electric Current - (Measured in Ampere) - Electric Current is the time rate of flow of charge through a cross sectional area.
Radius of Ring - (Measured in Centimeter) - 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
Radius of Ring: 6 Millimeter --> 0.6 Centimeter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mring = ([Permeability-vacuum]*i)/(2*rring) --> ([Permeability-vacuum]*2.2)/(2*0.6)
Evaluating ... ...
Mring = 2.30383461263252E-06
STEP 3: Convert Result to Output's Unit
2.30383461263252E-06 Tesla -->2.30383461263252E-06 Weber per Square Meter (Check conversion here)
FINAL ANSWER
2.30383461263252E-06 2.3E-6 Weber per Square Meter <-- Field at Center of Ring
(Calculation completed in 00.004 seconds)

Credits

Created by Aditya Ranjan
Indian Institute of Technology (IIT), Mumbai
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National Institute Of Technology (NIT), Hamirpur
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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 Ring Formula

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

How the formula arises ?

We can use the Biot-Savart law to find the magnetic field due to a current. We first consider arbitrary segments on opposite sides of the loop to qualitatively show by the vector results that the net magnetic field direction is along the central axis from the loop. From there, we can use the Biot-Savart law to derive the expression for magnetic field.
The magnetic field lines will be less denser in the region near the circumference of the loop than at the center. Thus, the magnetic field will be stronger at the center of the loop than in the region near the circumference.

How to Calculate Magnetic Field at Center of Ring?

Magnetic Field at Center of Ring calculator uses Field at Center of Ring = ([Permeability-vacuum]*Electric Current)/(2*Radius of Ring) to calculate the Field at Center of Ring, the Magnetic field at center of ring is given by B=μ0I/2R(at the center of the loop), where R is the radius of the loop. RHR-2 gives the direction of the field about the loop. Field at Center of Ring is denoted by Mring symbol.

How to calculate Magnetic Field at Center of Ring using this online calculator? To use this online calculator for Magnetic Field at Center of Ring, enter Electric Current (i) & Radius of Ring (rring) and hit the calculate button. Here is how the Magnetic Field at Center of Ring calculation can be explained with given input values -> 2.3E-6 = ([Permeability-vacuum]*2.2)/(2*0.006).

FAQ

What is Magnetic Field at Center of Ring?
the Magnetic field at center of ring is given by B=μ0I/2R(at the center of the loop), where R is the radius of the loop. RHR-2 gives the direction of the field about the loop and is represented as Mring = ([Permeability-vacuum]*i)/(2*rring) or Field at Center of Ring = ([Permeability-vacuum]*Electric Current)/(2*Radius of Ring). Electric Current is the time rate of flow of charge through a cross sectional area & 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 Ring?
the Magnetic field at center of ring is given by B=μ0I/2R(at the center of the loop), where R is the radius of the loop. RHR-2 gives the direction of the field about the loop is calculated using Field at Center of Ring = ([Permeability-vacuum]*Electric Current)/(2*Radius of Ring). To calculate Magnetic Field at Center of Ring, you need Electric Current (i) & Radius of Ring (rring). With our tool, you need to enter the respective value for Electric Current & 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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