A thin iron ring with mean diameter, `d=50 cm`. supports a winding consisting of 800 turns, with current 3A. The ring has a cross-cut of width 2.0 mm. The permeability of iron is (graph between B and H is given):

Options

A. `10^(3)`
B. `2xx10^(3)`
C. `3xx10^(3)`
D. `4xx10^(3)`

Answer

D

Explanation

For small gap, total line integral of `vec(H)` is
`int mu_(0)vec(H)vec(d)l=mu_(0)NI-Bb`
or `B=(mu_(0)NI)/b-(pidmu_(0)H)/b`
After solving, we get
`B=1.51-0.987 H(kA//m)`
`B` and `H` are also related to given graph. The required values of `B` and `H` must simultaneously satisfy both the relations. Solving this system of equation means of plotting, we get,
`B=1.25T`
`H=0.26 kA//m`
`mu=B/(mu_(0)H)=4xx10^(3)`