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

Write dimensional formula for induced emf.

Accepted Answer

Induced emf:- It is state that emf induced in coil having $N$ turn is directly proportional to rate of change of flux with respect to time. Induced current in the circuit is opposing the change in magnetic flux.

An emf is induced in the coil when a bar magnet is pushed in and out of it. Emfs of opposite signs are produced by motion in opposite directions, and the emfs are also reversed by reversing poles. The same results are produced if the coil is moved rather than the magnet—it is the relative motion that is important.

Electromotive Force, $E M F (ε) = W o r k D o n e \times [C h a r g e] - 1 . . . . (1)$

Since, Work Done $=$ Force $\times$ displacement

= Mass × acceleration × displacement $= [M] \times [M^{0} L^{1} T^{- 2}] \times [L]$

Therefore, the dimensional formula of work done $= M^{1} L^{2} T^{- 2} . . . . (2)$

And, Charge $=$ current $\times$ time

$∴$ The dimensional formula of charge $= I^{1} T^{1} . . . . (3)$

On substituting equation $(2)$ and $(3)$ in equation $(1)$ we get,

Electromotive Force $= W o r k D o n e \times {[C h a r g e]}^{- 1} .$

Or, $ε = [M^{1} L^{2} T^{- 2}] \times [I^{1} T^{1}] - 1 = [M^{1} L^{2} T^{- 3} I^{- 1}] .$

Therefore, Electromotive Force or EMF is dimensionally represented as $[M^{1} L^{2} T^{- 3} I^{- 1}] .$

The dimension of emf $E$ is, $[M L^{2} T^{- 3} A^{- 1}]$ .

Write dimensional formula for induced emf.

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