The dimensional formula of frac{1}{2}epsilon_ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The expression $\frac{1}{2}\epsilon_0 E^2$ represents the energy density of an electric field, which is defined as energy per unit volume.Dimensio

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) The expression $\frac{1}{2}\epsilon_0 E^2$ represents the energy density of an electric field, which is defined as energy per unit volume.Dimensions of energy = $[ML^2 T^{-2}]$.Dimensions of volume = $[L^3]$.Therefore, dimensions of energy density = $\frac{[ML^2 T^{-2}]}{[L^3]} = [ML^{-1} T^{-2}]$.Comparing this with $[M^a L^b T^c]$, we get $a = 1$, $b = -1$, and $c = -2$.Now, calculating the value of $2a - b + c$:$2(1) - (-1) + (-2) = 2 + 1 - 2 = 1$.

The dimensional formula of $\frac{1}{2}\epsilon_0 E^2$ ($\epsilon_0 = $ permittivity of vacuum and $E = $ electric field) is $M^a L^b T^c$. The value of $2a - b + c$ is . . . . . . .

Similar Questions

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

Dimensions of time in power are

Define dimensional formula and dimensional equation by using suitable examples.

Dimensional formula for torque is

Force $F = P \cos(Ax) + Q \sin(Bt)$,where $x$ and $t$ are displacement and time respectively. Which one of the following physical quantities has the dimensions of $\left[\frac{B}{A}\right]$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module