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

Question

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 (A)  (B/v)  (B)  (v/B)  (C)  √(v/B)  (D)  √(B/v)

Tardigrade Admin · Accepted Answer

The time period of electron moving in a circular orbit

T = \frac{circumference of circular path}{speed}

= \frac{2 π r}{v}

and equivalent current due to electron flow

I = \frac{e}{T} = \frac{e}{( 2 π r / v )} = \frac{e v}{2 π r}

Magnetic field at centre of circle

B = \frac{μ _{0} I}{2 r} = \frac{μ _{0} e v}{4 π r ^{2}}

\Rightarrow r \propto \frac{v}{B}

Q. 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

$\frac{B}{v}$

$\frac{v}{B}$

$\frac{v}{B}$

$\frac{B}{v}$

Q. 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

vB​

Bv​

Bv​​

vB​​

The time period of electron moving in a circular orbit T= speed circumference of circular path ​ =v2πr​ and equivalent current due to electron flow I=Te​=(2πr/v)e​=2πrev​ Magnetic field at centre of circle B=2rμ0​I​=4πr2μ0​ev​ ⇒r∝Bv​​

Q. 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

$\frac{B}{v}$

$\frac{v}{B}$

$\frac{v}{B}$

$\frac{B}{v}$