Chapter 21 Electromagnetic Induction, Problems 1, 2, 4, 7, 9, 12, 13, 18, 23, 25

Chapter 21, Problems 1, 2, 4, 7, 9, 12, 13, 18, 23, 25

Chapter 21, problem 1. A circular area with a radius of x₁ cm lives in the x-y plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = x₂ T that point

(a)    in the +z direction?

(b)   at an angle of x₃ᵒ from the +z direction?

(c)    in the +y direction?

Chapter 21, problem 2. The magnetic field B in a certain region is x₁ T, and its direction is that of the +z axis in figure 21.47.

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(a) What is the magnetic flux across the surface abcd in the figure?

(b) What is the magnetic flux across the surface befc?

(c) What is the magnetic flux across the surface aefd?



(d) What is the net magnetic flux through all five surfaces that enclose the shaded volume?

Chapter 21, Problem 4. A single loop of wire with an area of x₁ m² is in a uniform magnetic field that has an initial value of x₂ T, is perpendicular to the plane of the loop, and is decreased with the constant rate of x₃ T/s.
(a) What emf is induced in this loop?

(b) If the loop has a resistance of x₄ Ω, find the current induced in the loop.

Chapter 21, problem 7.  A closely wound rectangular coil of N turns has dimensions of x₁ cm by x₂ cm. The plane of the coil is rotated from a position where it makes an angle of x₃ᵒ with a magnetic field of x₄ T to a position perpendicular to the field. The rotation takes x₅ s.
What is average emf induced on the coil?

Chapter 21, Problem 9

A x₁ cm × x₂ cm rectangular circuit containing a x₃ Ω resistor is perpendicular to a uniform magnetic field that start out at x₄ T and steadily decreases at x₅ T/s. While this field is changing, what does the ammeter read?  (What is electric current in the circuit?)

Chapter 21, Problem 12

A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as in the figure. Terminals a and b of winding A may be connected to a battery through a reversing switch. State whether the induced current in the resistor R is from left to right or from right to left in the following circumstances:
(a) The current in winding A is from a to  b and is increasing.
(b) The current in winding A is from b to a and is decreasing.
(c) The current in winding A is from b to a and is increasing.

Chapter 21, Problem 13

A circular loop of wire is in a spatially uniform magnetic field, as shown in the figure.
The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when

(a)    B is increasing;

(b)   B is decreasing;

(c)    B is constant with a value of B₀.
Explain your reasoning.

Chapter 21, Problem 18

A bar magnet is held above a circular loop of wire as shown in the figure. Find the direction (clockwise or counterclockwise, as viewed from below the loop) of the current induced in this loop in each of the following cases:

(a)    The loop is dropped.

(b)   The magnet is dropped.

(c)    Both the loop and magnet are dropped at the same instant.

Chapter 21, Problem  23

You’re driving at x₁ km/h in a direction x₂° east of north, in a region where the earth’s magnetic field of x₃ × 10^-5 T is horizontal and points due north. If your car measures x₄ m from its underbody to its roof, calculate the induced emf between roof and underbody. (You can assume the sides of the car are straight and vertical.) Is the roof of the car at a higher or lower potential than the underbody?

Chapter 21, Problem 25

The conducting rod ab shown in Figure 21.61 makes frictionless contact with metal rails ca and db. The apparatus is in a uniform magnetic field of x₁ T, perpendicular to the plane of the figure.
(a) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed x₂ m/s.

(b) In what direction does the current flow in the rod?

(c) If the resistance of the circuit abdc is a constant x₃ Ω, find the magnitude and direction of the force required to keep the rod moving to the right with a constant speed of x₄ m/s.