#### Fields And Waves

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

Lightning strikes can happen when there is a large potential difference between a cloud and the ground. The energy transferred during one lightning strike is 1.6 × 10⁰ J.A charge of 23.7 C moves between the cloud and the ground in a time t.The magnitude of the current is 3.09 × 104 A. Assume that the potential difference between the cloud and the ground is constant. Calculate t. Calculate the potential difference between the cloud and the ground. A power station has an electrical output of 1300 MW. Calculate the time taken for the power station to transfer 1.6 × 10⁰ J.

16) What are the parameters of the plane wave in good conductors? What is the relationship between ?

(a) What are the major differences between the Fourier Transform and the Fourier Series? (b) What is the physical interpretation of the frequency response function H(f)?

1. Point charges 5 nC and -2 nC are located at points (2,0, 4) and (-3,0,5), respectively. Find the y-component of E(1,-3,7) in free space.

A diffraction grating of width 42 mm has 12 000 lines. Monochromatic light is incident normally on the grating. The angle between the two second-order diffraction maxima is 41.4°. Calculate the wavelength of the incident light.

(n) r at the load. (b) Zin at the input to the transmission line. (c) The input voltage Vi and input current i.

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?

Two students do an experiment to determine the resistance per unit length of a metal wire. Student A uses a metre ruler to make a single measurement of the length of the wire She records a value of 625 mm. She measures the resistance of the wire as 5.3 ± 0.3 0. Show that the percentage uncertainty in the length of the wire is approximately 0.2%. Determine, in 2 m, the student's value for resistance per unit length and the absolute uncertainty in her calculated value. Student B determines values of resistance R for a range of lengths / for the wire and uses them to plot a graph. Determine, using the gradient of the graph, the resistance per unit length of the wire in ohms -1 The method used by student B is better than the method used by student A.Suggest two reasons why

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?