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Question

An iron rod of volume 104m3 and relative permeability 1000 is placed inside a long solenoid wound with 5 turns/cm. If a current of 0.5A is passed through the solenoid, then the magnetic moment of the rod is

A
10Am2
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B
15Am2
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C
20Am2
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D
25Am2
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Solution

The correct option is D 25Am2
We have B=μ0H+μ0I

or I=Bμ0Hμ0 or I=μHμ0Hμ0=(μμ01)H

I=(μr1)H

For solenoid of n-turns per unit length and current i
H=ni

I=(μr1)ni=(10001)×500×0.5

I=2.5×105Am1

Magnetic moment M=IV

M=2.5×105×104=25Am

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