5.16 An air-filled rectangular waveguide is designed to transmit signals in the TE,g mode in the frequency band 5 GHz to 10 GHz. The waveguide is then filled with a material with relative dielectric constant equal to 4. In which of the following frequency bands can this waveguide be used to transmit a signal? (a) 20 GHz to 40 GHz (b) 10 GHz to 20 GHz (c) 1.25 GHz to 2.5 GHz (d) 2.5 GHz to 5 GHz

Consider a TE mode in a rectangular wave guide with a-2b (refer to figure in problem 1).Analyze the following statements • The electric field of the TE10 mode has only component • The H field of the TE10 mode is always perpendicular to the electric field E In all TE modes the electric field is always parallel to one of the wavegulde walls in any arbitrary cross section Select] In all TE modes the electric field is zero in the reglon very close to the waveguidewalls • For any arbitrary cross section in the wave guide, the electric field of the TE20 mode is always orlented exclusively in the positive direction or in the negative direction • The Index "m" in the TEmn modes indicates

State and explain one piece of evidence that shows that energy levels in atoms are discrete.

The diagram shows the spectrum for an X-ray tube. The minimum wavelength Amin of X-rays emitted from the X-ray tubecan be reduced by

Which statement about dispersion in optical fibres is not correct?

The maximum kinetic energy Ek(max) of the photoelectrons is measured for a range ofvalues off.unod is 82 x 10-19 J. The work function of the metal used is 8.2 x 10-1⁹ J. \text { Which graph shows the variation of } E_{\mathrm{k}(\max )} \text { with } f \text { ? }

A) What is the temperature of the outer surface of a star if the the peak wavelength emitted by surface of the star is170 nm? B) Consider the (continuous) spectra of light emitted by two different stars shown below. 1. Estimate the temperatures of these stars. 2. What would be the likely colors of these stars?

A student uses multimeters to measure the potential difference and the current in a circuit.The battery has an emf of 6.0 V and negligible internal resistance.

The speed of sound in air is 330 m s™¹. The loudspeakers are in phase and emit sound of frequency 660 Hz. The phase difference between the waves arriving at P from S₁ and S₂ is:

1. Let P = P(x, y, z), Q = Q(x, y, z), and R = R(x, y, z) be functions of three variables defined on a subset E of space. A vector field over E is defined as the function F(x, y, z) = P(x, y, z) + Q(x, y, z) + R(x, y, z). Determine whether the provided statement is true or false. 2. The gradient of a function f is an example of a vector field. Determine whether the provided statement is true or false. 3. Consider the vector field F(x, y) = xi + 2yj. Which of the following vector fields correctly graphs F(x, y)? Choose the correct vector field. 4. Consider the vector field F = F(x, y) = yi-j. Which of the following vector fields correctly graphs F(x, y)? Choose the correct vector field. 5. Consider the vector field F = F(x, y) = 2i. Which of the following vector fields correctly graphs F(x, y)? Choose the correct vector field. 6. Consider the vector field F = F(x, y) = -4i + 3j. Which of the following vector fields correctly graphs F(x, y)? Choose the correct vector field. 7. Consider the vector field F = F(x, y, z) = zk. Which of the following vector fields correctly graphs F(x, y, z)? Choose the correct vector field. 8. Consider the vector field F = F(x, y, z) = xi. Which of the following vector fields correctly graphs F(x, y, z)? Choose the correct vector field. 9. Find the gradient vector field of function f. f(x,y) = xe^13y (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) 10. Find the gradient vector field of function ƒ. f(x, y, z) = x^7y + 4xyz³ (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) 11. (a) Which of the following correctly describes the vector field F(x, y) = -yi + xj? F(x, y) is a set of vectors tangent to circles centered at the origin. O parallel to the y-axis. O parallel to the x-axis. O parallel to radius vectors of circles centered at the origin. (b) Which of the following correctly describes the magnitude of a vector in the field F(x, y) = -yi + xj? The magnitude of each vector in the field O is proportional to the distance of the vector from the x-axis. O equals the radius squared of the circle. O equals the radius of the circle. O is proportional to the distance of the vector from the y-axis. 12. Consider a very small object of mass m kg. The distance from this object is denoted by r and measured in meters (m). The gravitational potential due to the mass m is the scalar function u = - Gr, where G = 6.67 x 10-¹¹ N m²/kg² and r = xi + yj + zk. If the gravitational field g = -Vu, then what does g equal in terms of G, m, r, and r?