Question

A charge particle $q$ released at a distance $R_0$ from the infinite long wire of linear charge density $\lambda$. then velocity at distance $R$ from the wire will be proportional to:

• A. $R^3$
• B. $e^{R/R_0}$
• C. $R^2$
• D. ${\left[\ell n\left(\frac{R}{R_0}\right)\right]}^{1/2}$

Answer 1

The correct option is D ${\left[\ell n\left(\frac{R}{R_0}\right)\right]}^{1/2}$

$\Delta KE+\Delta U=0$
$(\frac{1}{2}m{v}^2-0)+q(v_f-v_i)=0$
$\frac{1}{2}m{v}^2+q[-2k\lambda \ell n\left(\frac{R}{R_0}\right)]=0$
$\frac{1}{2}m{v}^2=2k\lambda q\ell n\left(\frac{R}{R_0}\right)$
$v={\left[\frac{4k\lambda q}{m}\ell n\left(\frac{R}{R_0}\right)\right]}^{1/2}$