Search for question
Question

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?

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9


Most Viewed Questions Of Fields And Waves

5.3 The circuit shown in Fig. P5.3 uses two identical springs to support a 10-cm-long horizontal wire with a mass of 20 g. In the absence of a magnetic field, the weight of the wire causes the springs to stretch a distance of 0.2 cm each. When a uniform magnetic field is turned on in the region containing the horizontal wire, the springs are observed to stretch an additional 0.5 cm each. What is the intensity of the magnetic flux density B? The force equation for a spring is F = kd, where k is the spring constant and d is the distance it has been stretched.


Figure 8 shows a simple pendulum suspended from a ceiling that is too high to reach. The height of the ceiling is H. The centre of mass of the pendulum bob is a distance h from the floor when the pendulum is in the rest position. A student uses the pendulum to determine H. The relationship between h and the period T of the pendulum is: T=2 \pi \sqrt{\frac{H-h}{g}} The student wants to use a graphical method to determine both H and g. Describe the procedure that the student should use to collect data that produce accurate determinations of H and g.[3 marks] Describe how the data can be analysed using a straight-line graph to determine H and g.[2 mark


A batch of leather after drying weighs 500 kg and contains 6% moisture. During the process, leather loses 60% of its original weight. O Draw the flowsheet for this process. Calculate the original moisture content of the leather in terms of kg of H2O/kg of dry leather. Calculate kg of H20 removed/kg of dry leather. ) H2O removed as percent of the original water.


5.12 Design an air-filled rectangular waveguide to be used for transmission of electromagnetic power at 2.45 GHz. This frequency should be at the middle of the operating frequency band. The design should also allow maximum power transfer without sacrificing the operating bandwidth. Find the maximum power the waveguide can transmit. Use a safety factor of 10. Neglect ohmic loss. The breakdown E in air is assumed to be 2 x 10^6 V/m.


5.7 An 8 cm x 12 cm rectangular loop of wire is situated in the x-y plane with the center of the loop at the origin and its long sides parallel to the x-axis. The loop has a current of 50 A flowing clockwise (when viewed from above). Determine the magnetic field at the center of the loop.


An electric current is passed through a fluorescent tube. Electrons and ions collide with mercury gas in the fluorescent tube, raising the mercury atoms to higher energy levels. Describe how a fluorescent tube produces visible light. Suggest how this happens. The resistance of the tube decreases when the potential difference across it isincreased.


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?


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.


*5.10 An AM radio in an automobile cannot receive any signal when the car is inside a tunnel. Why? Let us assume that the tunnel is the Lincoln Tunnel, which was built in 1939 under the Hudson River in New York. Figure P 5.10 shows a cross section of the Lincoln Tunnel.


1A heating element in an electric heater consists of a coil of wire.The heating element transfers a power of 1.00 kW when connected directly to a mains supply of 230 V. Show that the resistance of the element is approximately 53 2. The element is made from wire that has a radius of 0.137 mm and a resistivity of 4.9 × 1072 m. Calculate the length of wire needed for the element. The electric heater contains two elements, each of resistance 53 ohms There is also a 230 V lamp to show when the heater is working. The power transferred by the lamp is negligible. The resistivity of the wire does not vary with temperature. Draw circuit diagrams to show how the components can be connected to transfer: • the maximum possible power using both elements• the minimum possible power using both elements.State, for each circuit, the total power transferred by the heater.