# Ampere's Law Formula

Ampere’sÂ lawÂ cameÂ toÂ existenceÂ inÂ 1826. The law talks about the sum of the magnetic field across a closed hoop which is carrying current.Â Ampere’sÂ lawÂ canÂ beÂ usefulÂ whenÂ measuringÂ aÂ highÂ

degreeÂ ofÂ symmetryÂ forÂ magneticÂ fieldsÂ withÂ currentÂ distributions.

## Ampereâ€™s Law Formula

 $$\begin{array}{l}\oint \vec{B}\vec{dl}=\mu _{0}I\end{array}$$

### Notations Used In Ampereâ€™s Law Formula

• B is the magnetic field
• L is the infinitesimal length
• I is the current flowing through the closed-loop
• Î¼ is the permeability

### Solved Example

Question 1: Compute the magnetic field of a long straight wire that has a circular loop with a radius of 0.05m. 2amp is the reading of the current flowing through this closed loop.

Solution:

Given

R = 0.05m

I = 2amp

Î¼0 = 4Ï€Ã—10-7N/A2

Ampereâ€™s law formula is

$$\begin{array}{l}\oint \vec{B}\vec{dl}=\mu _{0}I\end{array}$$

In the case of long straight wire

$$\begin{array}{l}\oint \vec{dl}=2\pi R=2\times 3.14\times 0.05=0.314\end{array}$$

$$\begin{array}{l}B\oint \vec{dl}=\mu _{0}I\end{array}$$

$$\begin{array}{l}\vec{B}=\frac{\mu _0I}{2\pi R}\end{array}$$

$$\begin{array}{l}\vec{B}=\frac{4\pi \times 10^{-7}\times 2}{0.314}=8\times 10^{-6}\,T\end{array}$$

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