JEE MAIN - Physics (2021 - 27th July Evening Shift - No. 6)
Match List I with List II.
Choose the correct answer from the options given below
| 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
(a) $$\to$$ (iii), (b) $$\to$$ (ii), (c) $$\to$$ (iv), (d) $$\to$$ (i)
(a) $$\to$$ (iii), (b) $$\to$$ (iv), (c) $$\to$$ (ii), (d) $$\to$$ (i)
(a) $$\to$$ (iv), (b) $$\to$$ (ii), (c) $$\to$$ (iii), (d) $$\to$$ (i)
(a) $$\to$$ (iv), (b) $$\to$$ (iii), (c) $$\to$$ (ii), (d) $$\to$$ (i)
Explanation
q = CV
$$[C] = \left[ {{q \over V}} \right] = {{(A \times T)} \over {M{L^2}{T^{ - 2}}}}$$
$$ = {M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$
$$[E] = \left[ {{F \over q}} \right] = {{ML{T^{ - 2}}} \over {AT}}$$
$$ = ML{T^{ - 3}}{A^{ - 1}}$$
$$F = {{{q_1}{q_2}} \over {4\pi { \in _0}{r^2}}}$$
$$[{ \in _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$$
Speed of light $$c = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$$
$${\mu _0} = {1 \over {{ \in _0}{c^2}}}$$
$$[{\mu _0}] = {1 \over {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}]{{[L{T^{ - 1}}]}^2}}}$$
$$ = [{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}]$$
$$[C] = \left[ {{q \over V}} \right] = {{(A \times T)} \over {M{L^2}{T^{ - 2}}}}$$
$$ = {M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$
$$[E] = \left[ {{F \over q}} \right] = {{ML{T^{ - 2}}} \over {AT}}$$
$$ = ML{T^{ - 3}}{A^{ - 1}}$$
$$F = {{{q_1}{q_2}} \over {4\pi { \in _0}{r^2}}}$$
$$[{ \in _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$$
Speed of light $$c = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$$
$${\mu _0} = {1 \over {{ \in _0}{c^2}}}$$
$$[{\mu _0}] = {1 \over {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}]{{[L{T^{ - 1}}]}^2}}}$$
$$ = [{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}]$$
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