Which one out of the following materials is \(\textit{not}\) paramagnetic
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is:
Magnetic material is one that can repel or attract other materials. The process of attraction or repulsion of these materials depends on the arrangement of electrons, which is known as the magnetic moment of that material.
Diamagnetic - With regard to the susceptibility χ, a material is diamagnetic if χ is negative. These materials produce negative magnetization when they are placed in the magnetic field. When placed in a magnetic field, these diamagnetic materials are barely magnetized. Diamagnetic substances are the ones that are repelled by magnets.
Paramagnetic - In the presence of an external magnetic field, the substances that get weakly magnetized are known as paramagnetic substances. The magnetic dipoles align along the direction of the applied field, reinforcing and enhancing the magnetic field. These substances get weakly attracted to a magnet as they tend to move from a weaker magnetic field to a stronger one. The magnetization (M) of paramagnetic materials, discovered by Madam Curie, depends on the temperature (T) and the external magnetic field B.
M = C x (B/T)
Where M = Magnetization
C = Curie Constant
B = External magnetic field
T = Temperature
Ferromagnetic - The materials strongly attracted by the magnetic field are known as ferromagnetic materials.