Q13PE - College Physics (Urone)

Question

Show that units of V/m and N/m for electric field strength are indeed equivalent.

Step-by-Step Solution

Answer

The units V/m and N/m are equivalent.

Step 1: Principle

In a homogeneous electric field of magnitude E , the potential difference between two locations separated by a distance d  is

 $\mathbf{\Delta V}\mathbf{=}\mathbf{Ed}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{(1)}$

The electric force F_e at any point due to a test charge q and electric field $\overrightarrow{\mathrm{E}}$ is given by,

 $\overrightarrow{\mathbf{E}}\mathbf{=}\frac{{\overrightarrow{\mathbf{F}}}_{\mathbf{e}}}{\mathbf{q}}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{(2)}$

Step 2: Explanation

The electric field strength is, according to Equation (1), equal to:

 $\mathbf{E}\mathbf{=}\frac{{\mathbf{F}}_{\mathbf{e}}}{\mathbf{q}}$

Where F_e is measured in Newton and q is in Coulombs, therefore, the electric field strength is measured in Newton/Coulomb or N/C.

 

From equation (2), electric field strength is:

 $\mathbf{E}\mathbf{=}\frac{\mathbf{\Delta V}}{\mathbf{d}}$

Where $∆\mathrm{V}$ is measured in volts and d is measured in meters, the electric field strength is measured in volt/meter or V/m .

 

Hence, V/m is equivalent to N/m.