Question

Find the dimensions of (a) electric field E, (b) magnetic field B and (c) magnetic permeability μ₀ .
Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

(a) We know that the formula of Electric field E is :- 
 E= F/q 
 Now changing into dimensions.
 E= MLT⁻² / I.T
 E= MLT⁻³ I⁻¹ 
Hence the dimensional formula of Electric field is MLT⁻³I⁻¹ .


(B) We know that the formula of Magnetic field B is :- 
 Magnetic field, B= $\frac{F}{qv}$ 
Now changing into dimensions.
B = MLT⁻² / [IT] [LT⁻¹]
B=  MT⁻² I⁻¹
Hence the dimensional formula of Magnetic Field B is MT⁻²I⁻¹ .

(C) We know that the formula of Magnetic permeability is :-
μ₀ = (B× 2πa) / I 
μ₀ = [MT⁻²I⁻¹ × L] / I
μ₀ = MLT⁻² I⁻¹
Hence the dimensional formula of Magnetic permeability is MLT⁻² I⁻¹ .


Hope it helps.