Question 171:
easy7. A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{circ}$ is $W$. Now the torque required to keep the magnet in this new position is: (2016 – II)
Work done in rotating the magnet from equilibrium is $W = MB(1 - cos 60^{circ}) = frac{MB}{2}$, giving $MB = 2W$. The torque required in this position is $tau = MB sin 60^{circ} = (2W)left(frac{sqrt{3}}{2}right) = sqrt{3}W$.
Question 172:
easy8. A magnetic needle suspended parallel to a magnetic field requires $sqrt{3} text{ J}$ of work to turn it through $60^{circ}$. The torque needed to maintain the needle in this position will be: (2012 Mains)
Work done is $W = MB(1 - cos 60^{circ}) = frac{MB}{2} = sqrt{3}$, which implies $MB = 2sqrt{3} text{ J}$. The torque required is $tau = MB sin 60^{circ} = 2sqrt{3} times frac{sqrt{3}}{2} = 3 text{ J}$.
Question 173:
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 174:
easy29. Electromagnets are made of soft iron because soft iron has: (2010 Pre)
An electromagnet should easily magnetize when current is switched on and readily lose its magnetism when current is turned off. Thus, the material must have low retentivity and low coercivity.
Question 175:
easy30. Curie temperature is the temperature above which: (2008)
Curie temperature is the critical temperature above which thermal agitation destroys the domain structure of a ferromagnetic material, converting it into a paramagnetic material.
Question 176:
easy31. Nickel shows ferromagnetic property at room temperature. If the temperature is increased beyond Curie temperature, then it will show: (2007)
When a ferromagnetic substance like nickel is heated beyond its Curie temperature ($T_C$), domain alignment is disrupted by thermal energy, and it behaves as a paramagnetic substance.
Question 177:
easy32. Above Curie temperature: (2006)
At temperatures higher than the Curie temperature, spontaneous magnetization in ferromagnetic materials vanishes and the substance transforms into a paramagnetic material obeying Curie-Weiss law.
Question 178:
easy33. According to Curie’s law, the magnetic susceptibility of a substance at an absolute temperature T is proportional to: (2003)
According to Curie's law for paramagnetic substances, magnetic susceptibility is inversely proportional to absolute temperature $T$, i.e., $\chi = \frac{C}{T}$, or $\chi \propto 1/T$.
Question 179:
easy20. A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from: (2018)
When the diamagnetic rod moves out of the magnetic field, it modifies the magnetic flux through the electromagnet. To maintain the magnetic field and current against the back emf, the current source does extra work, which provides the gained gravitational potential energy.
Question 180:
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.