Define magnetization. State its SI unit and dimensions.
Magnetization is a vector quantity that represents the magnetic moment per unit volume of a material. Denoted by \( \mathbf{M} \), it indicates both the strength and direction of the magnetic field within the material.
The SI unit of magnetization is \( {A/m} \) (Ampere per meter), and its dimensional formula is: \[ [M] = [I L^{-1}] \] where \( I \) is the current and \( L \) is the length. \bigskip
Two magnets of equal magnetic moment (\( m_1 = m_2 \)) are placed as shown in the figure. If the magnetic field intensity at P due to magnet A1 is \( 2 \times 10^{-3} \, \text{Tesla} \), then find out the total magnetic field intensity at P due to both the magnets.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]