Which of the following physical quantities have the same dimensions?
Solution
<p>Electric displacement $(\overrightarrow D ) = {\varepsilon _0}\overrightarrow E$</p>
<p>$\Rightarrow [\overline D ] = [{\varepsilon _0}][\overline E ]$</p>
<p>$= [{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}][{M^1}{L^1}{A^{ - 1}}{T^{ - 3}}]$</p>
<p>$[\overline D ] = [{L^{ - 2}}{T^1}{A^1}]$</p>
<p>[Surface charge density] $= {{[Q]} \over {[A]}}$</p>
<p>$[\sigma ] = [AT{L^{ - 2}}]$</p>
<p>$\Rightarrow \overrightarrow D$ and $[\sigma ]$ have same dimensions</p>
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
This question is part of PrepWiser's free JEE Main question bank. 120 more solved questions on Current Electricity are available — start with the harder ones if your accuracy is >70%.