A particle of charge - q mass m moves in a circle of radius r around an infinitely long line charge of linear charge density +λ. Then time period will be: [ K =(1/4 π ε0)]

Question

A particle of charge - q mass m moves in a circle of radius r around an infinitely long line charge of linear charge density +λ. Then time period will be: [ K =(1/4 π ε0)] (A) T =2 π r √( m /2 k λ q ) (B) T =√(4 π2 m /2 k λ q ) (C) T =(1/2 π r ) √(2 k λ q / m ) (D) (1/2 π r) √(m/2 k λ q)

Tardigrade Admin · Accepted Answer

( mv 2/ r )= q (λ/2 π ε0 r ) v =√( q λ/2 π ε0 m )=√(2 kq λ/ m ) T =(2 π r / v )=2 π r √( m /2 kq λ)

Q. A particle of charge $- q &$ mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear charge density $+ λ$ . Then time period will be : $[K = \frac{1}{4 π ε _{0}}]$

$T = 2 π r \frac{m}{2 kλ q}$

$T = \frac{4 π ^{2} m}{2 kλ q}$

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

$\frac{1}{2 π r} \frac{m}{2 kλ q}$

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

Q. A particle of charge −q& mass m moves in a circle of radius r around an infinitely long line charge of linear charge density +λ. Then time period will be : [K=4πε0​1​]

T=2πr2kλqm​​

T=2kλq4π2m​​

T=2πr1​m2kλq​​

2πr1​2kλqm​​