Question 71:
easy9. A short bar magnet of magnetic moment $0.4 text{ J T}^{-1}$ is placed in a uniform magnetic field of $0.16 text{ T}$. The magnet is in stable equilibrium when the potential energy is: (2011 Mains)
For stable equilibrium, the angle between $vec{M}$ and $vec{B}$ is $theta = 0^{circ}$. The potential energy is $U = -MB cos 0^{circ} = -0.4 times 0.16 = -0.064 text{ J}$.
Question 72:
easy13. Due to earth’s magnetic field, the charged cosmic rays particles (1997)
At the equator, magnetic field lines are perpendicular to incoming charged particles, causing maximum magnetic deflection force. At the poles, field lines are nearly parallel, causing little to no deflection. Thus, particles require much higher energy to penetrate at the equator.
Question 73:
easy14. A vibration magnetometer placed in magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of $2text{ sec}$ in earth’s horizontal magnetic field of $24text{ microtesla}$. When a horizontal field of $18text{ microtesla}$ is produced opposite to the earth’s field by placing a current carrying wire, the new time period of magnet will be: (2010 Pre)
Time period is $T propto frac{1}{sqrt{B}}$. Initially $B_1 = 24 mutext{T}$. In the second case, the net field is $B_2 = 24 - 18 = 6 mutext{T}$. Therefore, $T_2 = T_1 sqrt{frac{B_1}{B_2}} = 2 times sqrt{frac{24}{6}} = 2 times 2 = 4text{ s}$.
Question 74:
easy15. A bar magnet having a magnetic moment of $2 times 10^4text{ JT}^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $B = 6 times 10^{-4}text{ T}$ exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction $60^{circ}$ from the field is: (2009)
Work done is given by $W = MB(1 - costheta)$. Substituting the values: $W = (2 times 10^4) times (6 times 10^{-4}) times (1 - cos 60^{circ}) = 12 times 0.5 = 6text{ J}$.
Question 75:
easy16. A bar magnet is oscillating in the Earth’s magnetic field with a period $T$. What happens to its period and motion if its mass is quadrupled? (2003)
The period of oscillation is $T = 2pisqrt{frac{I}{MB}}$. Moment of inertia $I propto m$. If mass is quadrupled, $I' = 4I$, so $T' = 2pisqrt{frac{4I}{MB}} = 2T$. The motion continues to be simple harmonic.
Question 76:
easy17. Two bar magnets having same geometry with magnetic moments $M$ and $2M$, are firstly placed in such a way that their similar poles are same side then its time period of oscillation is $T_1$. Now the polarity of one of the magnet is reversed then time period of oscillation is $T_2$, then: (2002)
In sum position, effective magnetic moment is $M_{text{net}} = 2M + M = 3M$, so $T_1 propto frac{1}{sqrt{3M}}$. In difference position, $M_{text{net}} = 2M - M = M$, so $T_2 propto frac{1}{sqrt{M}}$. Since $M_{text{net}}$ decreases, the period increases, meaning $T_1 < T_2$.
Question 77:
easy18. The work done in turning a magnet of magnetic moment $M$ by an angle of $90^{circ}$ from the meridian, is $n$ times the corresponding work done to turn it through an angle of $60^{circ}$. The value of $n$ is given by (1995)
Work done for $90^{circ}$ is $W_1 = MB(1 - cos 90^{circ}) = MB$. Work done for $60^{circ}$ is $W_2 = MB(1 - cos 60^{circ}) = frac{MB}{2}$. Thus, $W_1 = 2 W_2$, which gives $n = 2$.
Question 78:
easy19. An iron rod of susceptibility $599$ is subjected to a magnetising field of $1200text{ A m}^{-1}$. The permeability of the material of the rod is: ($mu_0 = 4pi times 10^{-7}text{ T m A}^{-1}$) (2020)
Relative permeability is $mu_r = 1 + chi = 1 + 599 = 600$. The permeability of the material is $mu = mu_r mu_0 = 600 times 4pi times 10^{-7} = 2400pi times 10^{-7} = 2.4pi times 10^{-4}text{ T m A}^{-1}$.
Question 79:
easy21. The magnetic susceptibility is negative for: (2016 – I)
Magnetic susceptibility $\chi$ is defined as $I/H$. Diamagnetic substances develop magnetization in a direction opposite to the applied magnetic field, so their magnetic susceptibility is negative.
Question 80:
easy22. There are four light weight rod samples A, B, C, D separately suspended by threads. A bar magnet is slowly brought near each sample and the following observations are noted:
(i) A is feebly repelled
(ii) B is feebly attracted
(iii) C is strongly attracted
(iv) D remains unaffected
Which one of the following is true? (2011 Pre)
Diamagnetic materials are feebly repelled (A), paramagnetic materials are feebly attracted (B), ferromagnetic materials are strongly attracted (C), and non-magnetic materials remain unaffected (D). Therefore, B is a paramagnetic material.