First slide

Magnetic properties of matter

Question

An iron rod of volume $10^{- 3} m^{3}$ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be:

Moderate

A

$5 \times 10^{2} A m^{2}$
B

$500 \times 10^{2} A m^{2}$
C

$0.5 \times 10^{2} A m^{2}$
D

$50 \times 10^{2} A m^{2}$

Solution

$B_{n e t} = B_{i n d u c e d} + B_{e x t e r n a l}$
$\Rightarrow μ_{0} μ_{r} H = μ_{0} I + μ_{0} H$
$\Rightarrow 1000 μ_{0} n i = μ_{0} (n i + I)$
$h e r e, I = i n t e n s i t y o f m a g n e t i z a t i o n a n d H = n i = M a g n e t i z i n g f i e l d$
$\Rightarrow I = 999 n i = 999 \times 1000 \times 0.5$
$\Rightarrow$ $m a g n e t i c m o m e n t o f t h e r o d = I \times v o l = 999 \times 500 \times 10^{- 3} = \frac{999}{2} = 499.5 \approx 5 \times 10^{2} A m^{2}$

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