Question 210: Electrostats & Capacitance

Question

Match List I with List II.

List - I

List - II

(a)
Capacitance, C
(i)
$${M^1}{L^1}{T^{ - 3}}{A^{ - 1}}$$

(b)
Permittivity of free space, $${\varepsilon _0}$$
(ii)
$${M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$$

(c)
Permeability of free space, $${\mu _0}$$
(iii)
$${M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$

(d)
Electric field, E
(iv)
$${M^1}{L^1}{T^{ - 2}}{A^{ - 2}}$$

Choose the correct answer from the options given below

Accepted Answer

q = CV
$$[C] = \left[ {{q \over V}} ight] = {{(A 	imes T)} \over {M{L^2}{T^{ - 2}}}}$$
$$ = {M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$
$$[E] = \left[ {{F \over q}} ight] = {{ML{T^{ - 2}}} \over {AT}}$$
$$ = ML{T^{ - 3}}{A^{ - 1}}$$
$$F = {{{q_1}{q_2}} \over {4\pi { \in _0}{r^2}}}$$
$$[{ \in _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$$
Speed of light $$c = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$$
$${\mu _0} = {1 \over {{ \in _0}{c^2}}}$$
$$[{\mu _0}] = {1 \over {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}]{{[L{T^{ - 1}}]}^2}}}$$
$$ = [{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}]$$

Answer

(a) $$	o$$ (iii), (b) $$	o$$ (ii), (c) $$	o$$ (iv), (d) $$	o$$ (i)

Answer

(a) $$	o$$ (iii), (b) $$	o$$ (iv), (c) $$	o$$ (ii), (d) $$	o$$ (i)

Answer

(a) $$	o$$ (iv), (b) $$	o$$ (ii), (c) $$	o$$ (iii), (d) $$	o$$ (i)

Answer

(a) $$	o$$ (iv), (b) $$	o$$ (iii), (c) $$	o$$ (ii), (d) $$	o$$ (i)

Electrostats & Capacitance

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