MCQ
The dimensions of permittivity ${\varepsilon _0}$ are
- A${A^2}{T^2}{M^{ - 1}}{L^{ - 3}}$
- ✓${A^2}{T^4}{M^{ - 1}}{L^{ - 3}}$
- C${A^{ - 2}}{T^{ - 4}}M{L^3}$
- D${A^2}{T^{ - 4}}{M^{ - 1}}{L^{ - 3}}$
✓
Answer
Correct option: B.
${A^2}{T^4}{M^{ - 1}}{L^{ - 3}}$
b
(b) $F = \frac{1}{{4\pi {\varepsilon _0}}}\,\frac{{{q_1}{q_2}}}{{{r^2}}}$
(b) $F = \frac{1}{{4\pi {\varepsilon _0}}}\,\frac{{{q_1}{q_2}}}{{{r^2}}}$
$ \Rightarrow {\varepsilon _0} = \frac{{|{q_1}|\,|{q_2}|}}{{[F]\,[{r^2}]}} $ $= \frac{{[{A^2}{T^2}]}}{{[ML{T^{ - 2}}]\,[{L^2}]}} $ $= [{A^2}{T^4}{M^{ - 1}}{L^{ - 3}}]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A spring with spring constant $k $ is extended from $x = 0$to$x = {x_1}$. The work done will be
→Acetaldehyde and Acetone can be distinguished by
The average value of electric energy density in an electromagnetic wave is :
A rocket is moving in a gravity free space with a constant acceleration of $2 \ ms ^{-2}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \ m$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3 \ ms ^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2 \ ms ^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:
→Which of the following is not true about electric charge?
A ball of mass $100 \,g$ is dropped from a height $h =$ $10\, cm$ on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{ h }{2}$. The spring constant is.......... $Nm^{-1}$ . (Use $g=10\, ms ^{-2}$ )
→Water enters through end $A$ with speed ${v_1}$ and leaves through end $B$ with speed ${v_2}$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$ tube is horizontal and in case $ II$ it is vertical with end $ A $ upwards and in case $ III $ it is vertical with end $B$ upwards. We have ${v_1} = {v_2}$ for
→Two charges placed in air repel each other by a force of ${10^{ - 4}}\,N$. When oil is introduced between the charges, the force becomes $2.5 \times {10^{ - 5}}\,N$. The dielectric constant of oil is
→Let ${n_P}$ and ${n_e}$ be the number of holes and conduction electrons respectively in a semiconductor. Then
→$A$ uniform rod of mass $m$ and length $l$ hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinge when the rod becomes vertical is :
→