Question

In order to produce a flux of 100 μwb in an air gap of length 0.2 mm and area of cross-section is 1 cm², the MMF required is:
1. 500/π
2. 500 π
3. 250 π
4. 250/π

Answer 1

Correct Answer - Option 1 : 500/π

Magnetomotive force (MMF):

The current flowing in an electric circuit is due to the existence of electromotive force similarly magnetomotive force (MMF) is required to drive the magnetic flux in the magnetic circuit. The magnetic pressure, which sets up the magnetic flux in a magnetic circuit is called Magnetomotive Force.

The strength of MMF is equal to the product of the current and no. of turns of the coil

MMF can be expressed as

MMF = N I = (Flux) x (Reluctance)

The SI unit of MMF is ampere-turn (AT).

The Reluctance (S) is given as,

\(S=\frac{l}{\mu_0\mu_rA}\)

Calculation:

The Airgap length (l) = 0.2 mm = 0.2 × 10³ m

Cross-section area (A) = 1 cm2 = 10^-4 m²

Reluctance of airgap will be

\({S} = \frac{{{l}}}{{{\mu _o}A}} = \frac{{0.2 × {{10}^{ - 3}}}}{{4\pi × {{10}^{ - 7}} × 1 × {{10}^{ - 4}}}}=\frac{2}{4\pi \times 10^{-7}}\)

MMF = Flux × reluctance

\(MMF=100\times 10^{-6}\times \frac{2}{4\pi \times 10^{-7}}=\frac{500}{\pi}\ AT\)