Question

Sometimes the units for an electric field are written as N/C, while other times the units are written as V/m, using dimensional analysis show that N/C is equal to V/m.

a. True
b. False

Answer 1

N/C = V/m.

Step-by-step explanation:

The SI unit of electric field is N/C. Sometimes the units are written as V/m.

We know that,

1 V = 1 J/C

Using dimensional analysis,

The dimensional formula for Joules is [M¹L² T⁻²].

The dimensional form of coulomb is [M⁰ L⁰ T¹ I¹].

So,

J/C = [M¹L² T⁻³I¹] ...(1)

The dimensional formula of Newton is [M¹ L¹ T⁻²]

The dimensional form of coulomb is [M⁰ L⁰ T¹ I¹].

N/C= [M¹L² T⁻³I¹] ....(2)

From (1) and (2) it is clear that the N/C is equal to V/m.