Question

Figure shows two large cylindrical shells having uniform linear charge densities $+a\lambda$ and $-\lambda$ .Radius of inner cylinder as 'a' and that o outer cylinder is 'b' .A charged particle of mass m, charge q revolves in a circle of radius r.Then its speed 'v' is : (Neglect gravity and assume the radii of both the cylinders to be very small in comparision to their length)

• A. $\sqrt{\frac{\lambda q}{2\pi {\in }_{0}m}}$
• B. $\sqrt{\frac{2\lambda q}{\pi {\in }_{0}m}}$
• C. $\sqrt{\frac{\lambda q}{\pi {\in }_{0}m}}$
• D. $\sqrt{\frac{\lambda q}{4\pi {\in }_{0}m}}$

Answer 1

The correct option is A $\sqrt{\frac{\lambda q}{2\pi {\in }_{0}m}}$

Using Gauss's law for electrostatics,

Electric field at charged particle would be given as,

$E_r=\frac{\lambda }{2\pi {ϵ}_{o}r}$, towards the center

So centripetal force on particle is, $F=q{E}_r=\frac{\lambda q}{2\pi {ϵ}_{o}r}=\frac{m{v}^2}{r}$

$v=\sqrt{\frac{\lambda q}{2\pi {ϵ}_{o}m}}$

Option A is correct.