A particle of charge '$-q$' and mass '$m$' moves in a circle of radius '$r$' around an infinitely long line charge of linear density '$+\lambda$'. Then time period will be given as: (Consider k as Coulomb's constant)

(B) $\mathrm{T}=2 \pi \mathrm{r} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}$

(A) $\mathrm{T}^{2}=\frac{4 \pi^{2} \mathrm{~m}}{2 \mathrm{k} \lambda \mathrm{q}} \mathrm{r}^{3}$

(C) $T=\frac{1}{2 \pi r} \sqrt{\frac{m}{2 k \lambda q}}$

(D) $\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{m}}}$

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Electrostatics

A particle of charge '

- q

' and mass '

m

' moves in a circle of radius '

r

' around an infinitely long line charge of linear density '

+ λ

'. Then time period will be given as:
(Consider k as Coulomb's constant)

Answer: (B)

The electric field at perpendicular distance

r

from an infinite line charge of density

λ

E = \frac{2 k λ}{r}

This field supplies the centripetal force on the charge

- q

moving in a circle of radius

r

\frac{2 k λ q}{r} = m ω^{2} r

ω^{2} = \frac{2 k λ q}{m r ^{2}}

With

ω = \frac{2 π}{T}

(\frac{2 π}{T})^{2} = \frac{2 k λ q}{m r ^{2}}

T = 2 π r \frac{m}{2 k λ q}

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Single correct option