Magnetism and Matter Test -17

Toroid is a hollow circular ring on which a large number of turns of a wire are closely wound. Thus, in this case magnetic field is only confined inside the body of toroid.

So no magnetic field outside the toroid and magnetic field only inside the toroid.

In case of toroid, the magnetic field is in the form of concentric magnetic lines of force and there is no magnetic field outside the body of toroid. This is because the loop encloses no current. Thus, the magnetic moment of toroid is zero.

In other case, if we take r as a large distance outside the toroid, then \(m\propto {1\over r^3}\), which is not possible.

We know that a permanent magnet is a substance which at room temperature retain ferromagnetic property for a long period of time. The individual atoms in a ferromagnetic material possess a dipole moment as in a paramagnetic material. However, they interact with one another in such a way that they spontaneously align themselves in a common direction over a macroscopic volume i.e., domain.

Hence, in a permanent magnet at room temperature, domains are all perfectly aligned.

The electric field lines, do not form a continuous path while the magnetic field lines form the closed paths.

Gauss’s law states that \(\oint\limits_sE.ds={q\over \varepsilon_0}\) for electrostatic field. So, it does not contradict for electrostatic fields as the electric field lines do not form closed continuous path. According to Gauss’ law in magnetic field,

\(\oint\limits_sE.ds=0\)

It contradicts for magnetic field, because there is a magnetic field inside the solenoid and no field outside the solenoid carrying current but the magnetic field lines form the closed path.

According to the Curie law, the intensity of magnetisation (I) is directly proportional to the magnetic field induction and inversely proportional to the temperature (t) in kelvin.

So, I magnetisation \(\propto {B(magnetic\, field\, induction)\over t(temperature\, in\, kelvin)}\)

⇒ \({I_2\over I_1}={B_2\over B_1}\times {t_1\over t_2}\)      ...(i)

As given that: \(I_1=8Am^{-1}\), \(I_2=?\)

\(B_1\) = 0.6T, \(t_1\) = 4K

\(B_2\) = 0.2T, \(t_2\) = 16K

by putting the value of \(B_1\), \(B_2\), \(t_1\), \(t_2\) \(I_1\) in equation (i)

So, \({0.2\over 0.6}\times {4\over 16}={I_2\over 8}\)

We get, \(I_2=8\times {1\over12}\)

\(I_2={2\over3}A/m\)

As we know that, the magnetic intensity (H) outside any magnet is H = \(B\over \mu_0\)

For inside the magnet H = \(B\over \mu_0\mu_r\)

where \(\mu_r\) is the relative permeability of material.

Magnetic field lines for magnetic induction (B) form continuous lines so, lines of B are necessarily continuous across S.

Also, magnetic intensity (H) to magnetise varies for inside and outside the lump. So, lines of H cannot all be continuous across S.

Motion of charged particle produces magnetism and nature of magnetism depends on the motion of charge particle. The primary origin of magnetism lies in the fact that the electrons are revolving and spinning about nucleus of an atom, that gives rise to current called atomic current.

This atomic currents gives rise to magnetism. In atom, electrons revolving and spinning about nucleus of an atom is called intrinsic spin of electron.

As we know that, the magnetic field intensity H = nI,

where n = number of turns per metre of a solenoid and I = current.

And the magnetic induction

\(B=\mu_0 \mu_r nI\)      ...(i)

So, for solenoid H = nI

H = 1000 x 1 = 1000 Am   (\(\because\) given, n=1000)

So, H is a constant, then it is nearly unchanged.

From (i),

\(B=\mu_0 \mu_r nI\)

= \((\mu_0 nI)\mu_r=k\mu_r\)  (\(\therefore\) where, K = costant)

So, \(B\propto \mu_r\)

Hence, we find that, B varies with the variation in \(\mu_r\).

By curies law, when temperature of the iron core of solenoid or ferromagnetic material is raised beyond Curie temperature, then it behave as paramagnetic material, where,

Susceptibility \((\chi_m)_{Ferro1}=10^3\)

Susceptibility \((\chi_m)_{Para2}=10^{-5}\)

So, \({B_1\over B_2}\)  = \((\chi_m)_{Ferro1}\over (\chi_m)_{Para2}\) = \(10^3\over 10^{-5}\) = \(10^8\),

\(B_1=10^8B_2\)

or, \(B_2=10^{-8}B_1\).

Electrostatic shielding is the shielding which block the effects of an electric field.The conducting shell can block the effects of an external field on its internal content or the effect of an internal field on the outside environment.

As non existence of mono pole magnetic field lines cannot be stopped or shield. So, perfect shielding is not possible.

Magnetostatic shielding is done by using an enclosure made of a high permeability magnetic material to prevent a static magnetic field outside the enclosure from reaching objects inside it or to confine a magnetic field within the enclosure.

Angle of dip is the angle made by the total magnetic field of the earth with the surface of the earth.

The net magnetic field of the earth will be zero and it modelled by a point magnetic dipole at the centre, then it is in the same plane of geographical equator. So, the angle of dip at a specific point on the geographical equator will be zero, it is not zero at all point of geographical equator and it is bounded in a range from positive to negative value.