The dimension of permittivity - varepsilon - 0 - are - Take Q as the dimension of charge- M - -1 - L - -3 - T - 2 - Q - 2 - M - 1 - L - -2 - T - -2 - Q - -2 - M - -1 - L - 2 - T - -3 - Q - -1 -quad - M - -1 - L - 3 - T - -2 - Q - -2 -quad

Question

Toppr Admin · Accepted Answer

We know that electrostatic force is given as-F-KQ2r2We know that the dimension of force is -F-MLT-x2212-2-x2234-MLT-x2212-2-KQ2r2-K-ML3T-x2212-2Q-x2212-2K-14-x3C0-x3B5-o-x3B5-o-M-x2212-1L-x2212-3T2Q2

Column I	Column II
a) Angular momentum	g) ${M L}^{2} T^{- 2}$
b) Latent heat	h) ${M L}^{2} Q^{- 2}$
c) Torque	i) ${M L}^{2} T^{- 1}$
d) Capacitane	j) ${M L}^{3} T^{- 1} Q^{- 2}$
e) Inductance	k) $M^{- 1} L^{- 2} T^{2} Q^{2}$
f) Resistivity	l) $L^{2} T^{- 2}$

The dimension of permittivity ( $ε_{0}$ ) are ______. Take $Q$ as the dimension of charge.
$M^{- 1} L^{- 3} T^{2} Q^{2}$
$M^{1} L^{- 2} T^{- 2} Q^{- 2}$
$M^{- 1} L^{2} T^{- 3} Q^{- 1}$
$M^{- 1} L^{3} T^{- 2} Q^{- 2}$

We know that electrostatic force is given as:
$F = \frac{K Q^{2}}{r^{2}}$

We know that the dimension of force is $[F] = M L T^{- 2}$

$∴ M L T^{- 2} = \frac{K Q^{2}}{r^{2}} [K] = M L^{3} T^{- 2} Q^{- 2} K = \frac{1}{4 π ε_{o}} [ε_{o}] = M^{- 1} L^{- 3} T^{2} Q^{2}$

The dimension of permittivity (ε0) are ______. Take Q as the dimension of charge.M−1L−3T2Q2M1L−2T−2Q−2M−1L2T−3Q−1M−1L3T−2Q−2

We know that electrostatic force is given as:F=KQ2r2We know that the dimension of force is [F]=MLT−2∴MLT−2=KQ2r2[K]=ML3T−2Q−2K=14πεo[εo]=M−1L−3T2Q2

The dimension of permittivity ( $ε_{0}$ ) are ______. Take $Q$ as the dimension of charge.
$M^{- 1} L^{- 3} T^{2} Q^{2}$
$M^{1} L^{- 2} T^{- 2} Q^{- 2}$
$M^{- 1} L^{2} T^{- 3} Q^{- 1}$
$M^{- 1} L^{3} T^{- 2} Q^{- 2}$

We know that electrostatic force is given as:
$F = \frac{K Q^{2}}{r^{2}}$

We know that the dimension of force is $[F] = M L T^{- 2}$

$∴ M L T^{- 2} = \frac{K Q^{2}}{r^{2}} [K] = M L^{3} T^{- 2} Q^{- 2} K = \frac{1}{4 π ε_{o}} [ε_{o}] = M^{- 1} L^{- 3} T^{2} Q^{2}$