Question

Find the units of N/C equal to v/m?

Answer 1

No conversion needed , the magnitude of both the SI units are equal.

It can be proved as follows:-

V=E*d

Let, the unit of 'E' be N/C

Therefore,

V=N*m/C

OR, V/m =N/C

Hence , proved.

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Answer 2

Answer:

$\frac{V}{m} = \frac{N}{C}$ because when all units are converted to basic SI units, simplifying the equation will become $\frac{kg*m^{2} }{s^{2}} = \frac{kg*m^{2} }{s^{2}}$ which by further simplification becomes $J =J$ since both are SI units of J. See the explanation below.

Explanation:

Prove that $\frac{V}{m} = \frac{N}{C}$.

Given that the SI unit of:

$V=kg*m^{2} *s^{-3}*A^{-1}$

$m = m$

$N=kg*m*s^{-2}$

$C = A*s$

$J = kg*m^{2}*s^{-2}$

Substitute:

$\frac{V}{m} = \frac{N}{C}$

$\frac{kg*m^{2} *s^{-3}*A^{-1}}{m}=\frac{kg*m*s^{-2}}{A*s}$

Cross Multiply:

$(\frac{kg*m^{2}}{s^{3}*A}) A*s=(\frac{kg*m}{s^{2}})m$

Simplify:

$\frac{kg*m^{2} }{s^{2} } =\frac{kg*m^{2} }{s^{2} }$

$kg*m^{2}*s^{-2} = kg*m^{2}*s^{-2}$

Substitute:

$J=J$

Final Answer:

If    $\frac{V}{m} = \frac{N}{c}$ is equal to    $\frac{kg*m^{2} *s^{-3}*A^{-1}}{m}=\frac{kg*m*s^{-2}}{A*s}$  which can be simplified as    $kg*m^{2}*s^{-2} = kg*m^{2}*s^{-2}$ or    $J=J$, therefore, it is proved that    $\frac{V}{m} = \frac{N}{C}$.