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JIPMER 2007

Exam: JIPMER
Year: 2007
Subject: Physics
Chapter: Magnetic Effects of Current

JIPMER 2007 · Physics · Magnetic Effects of Current

An electron moves in a circular orbit with a uniform speed v . It...

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

Options

A $\frac{B}{v}$
B $\frac{v}{B}$
C $\sqrt{\frac{v}{B}}$
D $\sqrt{\frac{B}{v}}$

Correct answer

C. $\sqrt{\frac{v}{B}}$

Step-by-step solution

The time period of electron moving in a circular orbit

T=\frac{\text{ circumference of circular path }}{\text{ speed }} =\frac{2 \pi r}{v}

and equivalent current due to electron flow

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

Magnetic field at centre of circle

B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 e v}{4 \pi r^2} \Rightarrow r \propto \sqrt{\frac{v}{B}}

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