What are electromagnetic waves? Draw their propagation diagram. Show the electric field amplitude and magnetic field amplitude in the propagation diagram.
- Electromagnetic Waves: Electromagnetic waves are waves that consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation. They do not require a medium and can travel through a vacuum. These waves propagate with the speed of light \( c \) in a vacuum and carry energy and momentum. The electric field and magnetic field amplitudes are mutually perpendicular to each other and to the direction of wave propagation.
In the diagram:
- The electric field amplitude (E) oscillates in a plane.
- The magnetic field amplitude (B) oscillates perpendicular to the electric field.
AB is a part of an electrical circuit (see figure). The potential difference \(V_A - V_B\), at the instant when current \(i = 2\) A and is increasing at a rate of 1 amp/second is:
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $