JEE MAIN - Physics (2020 - 5th September Evening Slot - No. 16)
The quantities x = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$, y = $${E \over B}$$ and z = $${l \over {CR}}$$ are
defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and $${{\varepsilon _0}}$$, $${{\mu _0}}$$, - free space permittivity and permeability respectively. Then :
defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and $${{\varepsilon _0}}$$, $${{\mu _0}}$$, - free space permittivity and permeability respectively. Then :
Only y and z have the same dimension
x, y and z have the same dimension
Only x and y have the same dimension
Only x and z have the same dimension
Explanation
x = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$ = speed
$$ \therefore $$ [x] = [L1Tā1]
y = $${E \over B}$$ = speed
$$ \therefore $$ [y] = [L1Tā1]
z = $${l \over {CR}}$$ = $${l \over \tau }$$
$$ \Rightarrow $$ [z] = [L1Tā1]
So, x, y, z all have the same dimensions.
$$ \therefore $$ [x] = [L1Tā1]
y = $${E \over B}$$ = speed
$$ \therefore $$ [y] = [L1Tā1]
z = $${l \over {CR}}$$ = $${l \over \tau }$$
$$ \Rightarrow $$ [z] = [L1Tā1]
So, x, y, z all have the same dimensions.
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