Q: A 2.00-m long metal wire is formed into a square and placed in the horizontal $$xy-$$plane. A uniform magnetic field is oriented at $$30^\circ$$ above the horizontal with a strength of $$0.344\ \text{T}. $$What is the magnetic flux through the square due to this field?

$$0.0430\ \text{T} \cdot \text{m}^2$$

Q: Refer to the seventh image. A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $$0.40\ \text{T}. $$The length of the loop $$L is$$ $$0.16\ \text{m}$$ and its width $$w is$$ $$0.040\ \text{m}. $$What is the magnetic flux through the loop when the plane of the loop makes an angle of $$60^\circ$$ with the magnetic field?

$$2.2 \times 10$$^{-3}$$\ \text{T} \cdot \text{m}^2$$

Q: The area of a rectangular loop of wire is $$3.6 \times 10$$^{-3}$$\ \text{m}^2. $$The loop is placed in a uniform magnetic field that changes steadily from $$0.20\ \text{T} to$$ $$1.4\ \text{T} in$$ $$1.6\ \text{s}. $$The plane of the loop is perpendicular to the direction of the magnetic field. What is the magnitude of the induced emf in that loop?

$$2.7 \times 10$$^{-3}$$\ \text{V}$$

Question 1

A coil of wire containing $$N$$ turns is in an external magnetic field that is perpendicular to the plane of the coil and is steadily changing. If the rate of change of the magnetic field and the number of turns in the coil are both doubled, what will be the induced emf in the coil?

Accepted Answer

$$4\varepsilon$$

Question 2

A coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the sense of the induced current in this coil as the field fades?

Accepted Answer

The induced current flows clockwise initially, and then it flows counterclockwise before stopping.

Question 3

Refer to the first image. Two solenoids are close to each other, with the switch $$S$$ open. When the switch is suddenly closed, which way will the induced current flow through the galvanometer in the left-hand solenoid?

Accepted Answer

From right to left

Question 4

A 2.00-m long metal wire is formed into a square and placed in the horizontal $$xy-$$plane. A uniform magnetic field is oriented at $$30^\circ$$ above the horizontal with a strength of $$0.344\ 	ext{T}. $$What is the magnetic flux through the square due to this field?

Accepted Answer

$$0.0430\ 	ext{T} \cdot 	ext{m}^2$$

Question 5

Refer to the second image. A circular coil of copper wire is lying flat on a horizontal table. A bar magnet is held above the center of the coil with its south pole downward. The magnet is released from rest and falls toward the coil. As viewed from above, what is the direction of the current induced in the coil as the magnet approaches the coil?

Accepted Answer

Clockwise

Question 6

A bar magnet is oriented above a copper ring. If the magnet is pulled upward, what is the direction of the current induced in the ring, as viewed from above?

Accepted Answer

Counterclockwise

Question 7

Refer to the third image. The three loops of wire are all hanging in the same uniform magnetic field $$B$$ that is perpendicular to the page and does not vary with time. Loop 1 swings back and forth like a pendulum, Loop 2 rotates about a vertical axis, and Loop 3 oscillates up and down at the end of a spring. Which loop(s) will have an emf induced in them?

Accepted Answer

Loop 2

Question 8

Refer to the fourth image. Two parallel wires carry a current $$I in $$opposite directions, and this current is decreasing. A rectangular loop is centered between the wires. What is the direction of the induced current through the resistor $$R$$?

Accepted Answer

From b to a

Question 9

Refer to the fifth image. A C-shaped conductor is in a uniform magnetic field $$B$$ out of the page, and this field is increasing. What is the polarity of the induced emf in terminals $$X$$ and $$Y$$?

Accepted Answer

Y is positive and X is negative.

Question 10

Refer to the sixth image. A metal bar is in contact with a pair of metal parallel rails. A steady uniform magnetic field $$B$$, perpendicular to the plane of the rails and pointing outward from the page, is present. The bar is in downward motion with velocity $$
u. $$What is the direction of the induced current through the resistor $$R$$?

Accepted Answer

From a to b

Question 11

If the secondary coil of a transformer contains more loops than the primary coil, then it is a:

Accepted Answer

Step-up transformer.

Question 12

Refer to the seventh image. A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $$0.40\ 	ext{T}. $$The length of the loop $$L is$$ $$0.16\ 	ext{m}$$ and its width $$w is$$ $$0.040\ 	ext{m}. $$What is the magnetic flux through the loop when the plane of the loop makes an angle of $$60^\circ$$ with the magnetic field?

Accepted Answer

$$2.2 	imes 10$$^{-3}$$\ 	ext{T} \cdot 	ext{m}^2$$

Question 13

A closed flat loop conductor with radius $$2.0\ 	ext{m} is $$located in a changing uniform magnetic field. If the emf induced in the loop is $$2.0\ 	ext{V}$$, what is the rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies?

Accepted Answer

$$0.16\ 	ext{T/s}$$

Question 14

Refer to the eighth image. A wire and a $$10\ \Omega$$ resistor are used to form a circuit in the shape of a square with dimensions $$20\ 	ext{cm} by$$ $$20\ 	ext{cm}. A $$uniform but non-steady magnetic field is directed into the plane of the circuit. The magnitude of the magnetic field is steadily decreased from $$2.70\ 	ext{T} to$$ $$0.90\ 	ext{T} in a $$time interval of $$96\ 	ext{ms}. $$What is the induced current in the circuit, and what is its direction through the resistor?

Accepted Answer

$$75\ 	ext{mA}$$, from b to a

Question 15

The area of a rectangular loop of wire is $$3.6 	imes 10$$^{-3}$$\ 	ext{m}^2. $$The loop is placed in a uniform magnetic field that changes steadily from $$0.20\ 	ext{T} to$$ $$1.4\ 	ext{T} in$$ $$1.6\ 	ext{s}. $$The plane of the loop is perpendicular to the direction of the magnetic field. What is the magnitude of the induced emf in that loop?

Accepted Answer

$$2.7 	imes 10$$^{-3}$$\ 	ext{V}$$

Question 16

Refer to the ninth image. A conducting rod of length $$\ell = 25\ 	ext{cm} is $$placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of $$8.0\ \Omega. $$The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $$0.40\ 	ext{T} is $$applied perpendicular to and into the paper. An applied external force pulls the rod to the right with a constant speed of $$6.0\ 	ext{m/s}. $$What is the magnitude of the emf induced in the rod?

Accepted Answer

$$0.60\ 	ext{V}$$

Question 17

The primary coil of an ideal transformer has $$100$$ turns and its secondary coil has $$400$$ turns. If the AC current in the secondary coil is $$2\ 	ext{A}$$, what is the current in its primary coil?

Accepted Answer

$$8\ 	ext{A}$$

Question 18

A generator produces $$60\ 	ext{A} of $$current at $$120\ 	ext{V}. $$The voltage is usually stepped up to $$4500\ 	ext{V} by an $$ideal transformer and transmitted through a power line of total resistance $$1.0\ \Omega. $$Find the number of turns in the secondary if the primary has $$200$$ turns.

Accepted Answer

$$7500$$

Question 19

A circular coil of $$20$$ turns and radius $$5.0\ 	ext{cm} is $$placed with its plane oriented at $$90^\circ to a $$uniform magnetic field of $$0.10\ 	ext{T}. $$The field is now increased at a steady rate, reaching a value of $$0.50\ 	ext{T}$$ after $$4.0$$ seconds. What emf is induced in the coil?

Accepted Answer

$$0.016\ 	ext{V}$$

Question 20

A resistor and an inductor are connected in series to a battery. The battery is suddenly removed from the circuit and replaced by a wire to complete the circuit. The time constant for the new circuit represents the time required for the current to decrease to:

Accepted Answer

37% of the original value.

Electromagnetic Induction and Magnetic Flux: Step-by-Step Physics Guidance

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