Q. Two conducting sphere of radii r$_{1}$ and r$_{2 }$ are charged to the same surface charge density. The ratio of electric field near their surface is
A) $r_{1\ \ }^{2}$/ $r_{2}^{2}$
B) $r_{2\ \ }^{2}$/ $r_{1}^{2}$
C) $r_{1\ \ }^{\ }$/ $r_{2}^{\ }$
D) 1 : 1
Explanation
(d) As $\sigma_{1} = \sigma_{2}$
$\therefore\ \ \frac{Q_{1}}{4\pi r_{1}^{2}\ } = \frac{Q_{2}}{4\pi r_{2}^{2}\ }\ $
Or $\frac{Q_{1}}{4\pi{\varepsilon_{0}r}_{1}^{2}\ } = \frac{Q_{2}}{4\pi{\varepsilon_{0}r}_{2}^{2}\ }$
$\therefore\ \ \ E_{1} = E_{2}\ or\ {\ E}_{1}/E_{2}$=1
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.