A particle of charge $- q$ and mass $m$ moves in a circular orbit of radius $r$ about a fixed charge $+ Q$ . The relation between the radius of the orbit $r$ and the number of revolution per second $n$ is

r^{3} = \frac{Q q}{16 π^{3} ϵ_{0} m n^{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

r^{2} = \frac{Q q}{32 π^{3} ϵ_{0} m n^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r^{3} = \frac{Q q}{8 π^{3} ϵ_{0} m n^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r^{3} = \frac{Q q}{8 π^{3} ϵ_{0} m^{2} n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $r^{3} = \frac{Q q}{16 π^{3} ϵ_{0} m n^{2}}$
From circular dynamics,

$\frac{1}{4 π ϵ_{0}} \frac{Q q}{r^{2}} = m r ω^{2}$

$\Rightarrow \frac{1}{4 π ϵ_{0}} \frac{Q q}{r^{2}} = m r (2 π n)^{2}$

$∴ r^{3} = \frac{Q q}{16 π^{3} ϵ_{0} m n^{2}}$

Suggest Corrections

Similar questions

A particle of charge $- q$ and mass $m$ moves in a circular orbit of radius $r$ about a fixed charge $+ Q$ . The relation between the radius of the orbit $r$ and the time period $T$ is:

Q. A particle of charge -q & mass m moves in a circular orbit about a fixed charge +Q in a circle of radius r and time period T. which of the following may be correct

Q. A particle of mass

m

and carrying charge

- q_{1}

is moving around a charge

+ q_{2}

along a circular path of radius

r

. Find period of revolution of the charge

- q_{1}

Q. A charge q coulomb makes n revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in

N A^{- 1} m^{- 1}

Q. Suppose a particle

a

of charge

2 e

and mass

2 m_{e}

(

m_{e}

being mass of electron) revolves around the proton in nearest allowed circular orbit of radius r. If the radius of first Bohr orbit for the electron is

A_{0}

, then the relation between

r

and

a_{0}

Join BYJU'S Learning Program

A particle of charge −q and mass m moves in a circular orbit of radius r about a fixed charge +Q. The relation between the radius of the orbit r and the number of revolution per second n is

The correct option is A r3=Qq16π3ϵ0mn2From circular dynamics, 14πϵ0Qqr2=mrω2 ⇒14πϵ0Qqr2=mr(2πn)2 ∴ r3=Qq16π3ϵ0mn2

A particle of charge $- q$ and mass $m$ moves in a circular orbit of radius $r$ about a fixed charge $+ Q$ . The relation between the radius of the orbit $r$ and the number of revolution per second $n$ is

The correct option is A $r^{3} = \frac{Q q}{16 π^{3} ϵ_{0} m n^{2}}$
From circular dynamics,

$\frac{1}{4 π ϵ_{0}} \frac{Q q}{r^{2}} = m r ω^{2}$

$\Rightarrow \frac{1}{4 π ϵ_{0}} \frac{Q q}{r^{2}} = m r (2 π n)^{2}$

$∴ r^{3} = \frac{Q q}{16 π^{3} ϵ_{0} m n^{2}}$