Question

a point charge of q of mass m is placed at centre of a fixed ring of charge Q and radius R. what minimum velocity should be given to q so that it would reach far away from ring (i) if q is positive

Answer 1

Given that,

⟩ Charge of ring = Q

⟩ Charge of particle = q

⟩ Mass of particle = m

⟩ Radius of ring = R

We have to find magnitude of minimum required velocity which pushes point charge far away from ring$.$

❖ This question is completely based on the concept of mechanical energy conservation.

$\sf\dashrightarrow\:U_1+K_1=U_2+K_2$

$\sf\dashrightarrow\:\dfrac{1}{4\pi\epsilon_o}\cdot\dfrac{Qq}{R}+0=0+\dfrac{1}{2}mv^2$

$\sf\dashrightarrow\:v^2=\dfrac{2}{4\pi\epsilon_o}\cdot\dfrac{Qq}{mR}$

$\sf\dashrightarrow\:v^2=\dfrac{1}{2\pi\epsilon_o}\cdot\dfrac{Qq}{mR}$

$\dashrightarrow\:\underline{\boxed{\bf{\orange{v=\sqrt{\dfrac{1}{2\pi\epsilon_o}\cdot\dfrac{Qq}{mR}}}}}}$