Question

An electron is moving on a circular orbit of radius
r with speed v. It produces a magnetic field B at
its centre, then radius of circle is proportional to​

Answer 1

Answer:

Explanation:

Bv

vR

vB−−√

Bv−−√

Answer :

C

Solution :

Electric current corresponds to the revolution of electron is i=ev2πr Magnetic field due to circular current at the centre B=μ4π.2πir=μo4π.evr⇒

r=μ04π.evB−−−−−−√⇒r∝vB−−√

Answer 2

The radius of circle is proportional to​ $\sqrt{\dfrac{v}{B}}$

Explanation:

Given that,

Radius = r

Speed = v

magnetic field = B

We know that,

Electric current corresponds to the revolution of electron is

$i=\dfrac{ev}{2\pi r}$

Magnetic field due to circular current at the center is

$B=\dfrac{\mu}{4\pi} \dfrac{2\pi i}{r}$

Put the value of current

$B=\dfrac{\mu}{4\pi}\times\dfrac{2\pi\times ev}{r\times2\pi r}$

$B=\dfrac{\mu ev}{4\pi r^2}$

$r=\sqrt{\dfrac{\mu ev}{4\pi B}}$

$r\propto\sqrt{\dfrac{v}{B}}$

Hence, The radius of circle is proportional to​ $\sqrt{\dfrac{v}{B}}$

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Topic : magnetic field

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