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 a highÂ
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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