A particle of charge -q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density +λ. Then its time period is (. where .k=(1/4 π ε0))

Question

A particle of charge -q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density +λ. Then its time period is (. where .k=(1/4 π ε0)) (A) T=2 π r √(m/2 k λ q) (B) T2=(4 π2 m/2 k λ q) (C) T=(1/2 π r) √(2 k λ q/m) (D) T=(1/2 π r) √(m/2 k λ q)

Tardigrade Admin · Accepted Answer

(m v2/r)=q (λ/2 π ε0 r) ⇒ v=√(q λ/2 π ε0 m)=√(2 k q λ/m) T=(2 π r/v)=2 π r √(m/2 k q λ)

Q. A particle of charge $- q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear charge density $+ λ$ . Then its time period is $($ where $k = \frac{1}{4 π ε _{0}})$

$T = 2 π r \frac{m}{2 kλ q}$

$T^{2} = \frac{4 π ^{2} m}{2 kλ q}$

$T = \frac{1}{2 π r} \frac{2 kλ q}{m}$

$T = \frac{1}{2 π r} \frac{m}{2 kλ q}$

$\frac{m v ^{2}}{r} = q \frac{λ}{2 π ε _{0} r}$
$\Rightarrow v = \frac{q λ}{2 π ε _{0} m} = \frac{2 k q λ}{m}$
$T = \frac{2 π r}{v} = 2 π r \frac{m}{2 k q λ}$

Q. A particle of charge −q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density +λ. Then its time period is ( where k=4πε0​1​)

T=2πr2kλqm​​

T2=2kλq4π2m​

T=2πr1​m2kλq​​

T=2πr1​2kλqm​​