Question

A current in a solenoid produces a magnetising field of 167Amp m-1, what is the magnetic induction inside it if it has an iron core of magnetic susceptibility 5000?​

Answer 1

Concept:

The relation between magnetic induction, magnetic permeability and Magnetic field is given by the equation- B = μH​

Given:

Magnetising field, H = 167 A/m

Magnetic susceptibility, k = 5000

Find:

We need to determine the magnetic induction, B inside a solenoid having an iron core.

Solution:

The degree to which a substance can get magnetised by an external magnetic field is known as magnetic susceptibility.

In terms of permeabiity it is mathematically expressed as- k = μ/μ₀ - 1 where k = magnetic susceptibility, μ = magnetic permeability and μ₀ = permeabilty constant = 4π×10^-7

Therefore, μ = μ₀(k+1)

μ = 4π×10^-7 (5000+1)

μ = 62,812.4 × 10^-7 W/Am

We know, that the process through which a magnetic field from outside material or object makes it magnetic is called Magnetic induction. It is generally represented by the formula-

B = μH where B = magnetic induction, μ = magnetic permeability and H = Magnetising field

B = 62,812.4 × 10^-7 × 167

B = 0.8 Wb/m²

Thus, the magnetic induction is 0.8 Wb/m²

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