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Magnetic Field at the Centre of a Circular Loop
Concepts tested here
- Field of a revolving charge
All Questions
2005 AIPMT 1 question
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An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to :The revolving electron is equivalent to a current $I = \dfrac{e}{T}$, where the time period is $T = \dfrac{2\pi R}{v}$.
$I = \dfrac{ev}{2\pi R}$
Magnetic field at the centre of a circular current: $B = \dfrac{\mu_0 I}{2R}$
$B = \dfrac{\mu_0}{2R}\left(\dfrac{ev}{2\pi R}\right) = \dfrac{\mu_0 ev}{4\pi R^2}$
$\Rightarrow R^2 = \dfrac{\mu_0 ev}{4\pi B}$
$\Rightarrow R \propto \sqrt{\dfrac{v}{B}}$