Name: Electric Field: Time Varying Magnetic Field
Uploaded: 2019-07-19
Duration: 8 min 32 s
Description: Did you know that the cause of the movement of charges in a stationary circular conducting coil placed in a time-varying magnetic field is due to an induced...

Question

The dimensional formula of magnetic flux is

Accepted Answer

The dimensional formula is defined as the expression of the physical quantity in terms mass $(M)$ , length $(L)$ , time $(T)$ and ampere $(A)$ . Magnetic flux $(ϕ)$ refers to the number of magnetic field lines $(B)$ passing through a given area $(A)$ . Its SI unit is Weber $(Wb)$ . Mathematically it is represented as, $ϕ = BA$ .

We know that, when a charge particle $q$ enters a magnetic field $B$ with a velocity $v$ , it experiences a force which is equal to, $F = qvB$ . Here, $F$ is the force of a magnetic field, $q$ is the charge, $v$ is the particle's velocity, or, $B = \frac{F}{qv}$ . Hence,

Dimension of magnetic field is calculated using relation, $B = \frac{F}{qv}$

Dimensional formula of force, $(F) = [{MLT}^{- 2}]$

Dimensional formula of charge, $(q) = [AT]$

Dimensional formula of velocity, $(v) = [{LT}^{- 1}]$

Hence, the dimensional formula of $B$ is, $B = \frac{[{MLT}^{- 2}]}{[AT] [{LT}^{- 1}]} \Rightarrow [{MT}^{- 2} A^{- 1}]$

The dimensional formula of area is given as, $(A) = [L^{2}]$ . Therefore, the dimensional formula of magnetic flux is,

$BA = [{MT}^{- 2} A^{- 1}] [L^{2}] = [{ML}^{2} T^{- 2} A^{- 1}]$

The dimensional formula of magnetic flux is

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