S L Arora Solutions for Chapter: Magnetism, Exercise 1: Problems For Practice

A magnet placed in the north pointing north position, balances the earth's magnetic field at a point, which is $27 \mathrm{cm}$ from either pole. If it is broken into three pieces and one such piece is similarly placed, find the position of the neutral point.

The maximum value of permeability of $\mu$-metal $\left(77\% \mathrm{Ni},\mathrm{ }16\% \mathrm{Fe},\mathrm{ }5\% \mathrm{Cu},\mathrm{ }2\% \mathrm{Cr}\right)$ is $0.126\mathrm{ }\mathrm{T}\mathrm{ }{\mathrm{mA}}^{-1}$. Find the maximum relative permeability and susceptibility.

Find the percent increase in the magnetic field $B$B when the space within a current-carrying toroid is filled with aluminium. The susceptibility of aluminium is $2.1\times \mathrm{ }{10}^{-5}$.

The susceptibility of magnesium at $300 \mathrm{K}$ is $1.2\times {10}^{-5}$. At what temperature will the susceptibility increase to $1.8\times \mathrm{ }{10}^{-5}$.

An iron rod of $0.2\mathrm{ }{\mathrm{cm}}^2$ cross-sectional area is subjected to a magnetising field of $1200\mathrm{ }\mathrm{A}\mathrm{ }{\mathrm{m}}^{-1}$. The susceptibility of iron is $599$. Find the permeability and the magnetic flux produced.

A toroidal solenoid of mean radius $20 \mathrm{cm}$ has $4000$ turns of wire wound on a ferromagnetic core of relative permeability $800$. Calculate the magnetic field in the core for a current of $3 A$ passing through the coil. How does the field change, when this core is replaced by a core of bismuth?

An iron ring of mean circumferential length $30 \mathrm{cm}$ and cross-section $1 {\mathrm{cm}}^2$ is wound uniformly with $300$ turns of wire. When a current of $0.032 A$ flows in the windings; the flux in the ring is $2\times {10}^{-6}\mathrm{ }\mathrm{Wb}$. Find the flux density in the ring, magnetising field intensity and relative permeability of iron.

An iron ring having $500$ turns of wire and a mean diameter of $12 \mathrm{cm}$ carries a current of $0.3 A$. The relative permeability of iron is $600$. What is the magnetic flux density in the core ? What is the magnetisation field intensity? What part of the flux density is due to the electronic loop currents in the core?