# Ampere's Law Formula

Ampere’s law came to existence in 1826. The law talks about the sum of the magnetic field across a closed hoop which is carrying current. Ampere’s law can be useful when measuring high

degree of symmetry for magnetic fields with current distributions.

## Ampere’s Law Formula

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

### Notations Used In Ampere’s Law Formula

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

μ0 = 4π×10-7N/A2

Ampere’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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