Question

Find the dimensions and units of epsilon_0

Answer 1

Answer:

Hey mate,

According to Coulomb's Law:

F=(1/4πε₀)q1q2/r²

ε₀=(1/4πF) q1q2/r²

Dimension formula of F=M¹L¹T⁻²

Charge =q=IXT=AxT¹ where A= electric current

ε₀=(1/M¹L¹T⁻²)(AT¹xAT¹)/L²

ε₀=M⁻¹L⁻³T⁴A²

∴ Dimensional Formula of Epsilon naught= M⁻¹L⁻³T⁴A²

Epsilon Naught Unit: Farad per meter(in SI)

Answer 2

The unit and dimension as given below:

• The unit of epsilon is ∈=c²/Nm²
• Where c is charge q= current×time=(A)×(T)=AT
• Now calculate the dimension of force(N)= mass×acceleration
• Acceleration=LT⁻²
• Therefore dimension of force ML³T⁻²
• The dimension of epsilon is c²/Nm²
• (AT)²/ML³T⁻²
• That is [ML⁻³T⁴A]