Question

A large plate of uniform charge density is placed as shown, two cylinders of same volume are at distances $r$ & $2r$ respectively, if energy (electrostatic) stored in them are $U_A$ & $U_B$ respectively then,

• A. $U_A:U_B=4:1$
• B. $U_A:U_B=1:1$
• C. $U_A:U_B=1:4$
• D. $U_A:U_B=8:1$

Answer 1

The correct option is B $U_A:U_B=1:1$

Energy = Energy density $\times$ volume
$=\frac{1}{2}{\in }_0{E}^2\times \left(Volume\right)$
$\frac{U_A}{U_B}=\frac{\frac{1}{2}{\in }_0{E}_A^2\times Volume}{\frac{1}{2}{\in }_0{E}_B^2\times Volume}={\left(\frac{E_A}{E_B}\right)}^2=1:1$
Field is independent of distance in case of charged sheet.