Q: A plane surface with area $$A = 3.0 \times 10$$^{-4}$$\ \text{m}^2 is $$placed in a uniform magnetic field $$B at an $$angle of $$60^ ext{o} to $$the field. If the magnetic flux through the area is $$0.90\ \text{mWb}$$, what is the magnitude of the magnetic field?

$$B = 0.90\ \text{mWb} \div (3.0 \times 10$$^{-4}$$\ \text{m}^2 \cos 60^ ext{o}) = 6.0\ \text{T}$$

Q: A circular coil of wire with 500 turns and an average radius of $$4.00\ \text{cm} is $$placed at a $$60^ ext{o}$$ angle to a uniform magnetic field. The field changes at a rate of $$-0.200\ \text{T/s}. $$What is the magnitude of the resulting induced emf?

$$\varepsilon = 500 \times \pi \times (0.04)^2$ \times 0.200 \times \cos 60^ ext{o}$$

Q: In a slide-wire generator, a rod of length $$0.10\ \text{m}$$ moves at $$2.5\ \text{m/s} in a $$magnetic field of $$0.60\ \text{T}. $$What is the induced emf?

$$\varepsilon = 0.10 \times 2.5 \times 0.60 = 0.15\ \text{V}$$

Question 1

A credit card reader uses electromagnetic induction to read the magnetically encoded data on a card. Which principle explains how the changing magnetic field in the card's strip induces a current in the reader's coil?

Accepted Answer

Faraday's Law of Induction

Question 2

A plane surface with area $$A = 3.0 	imes 10$$^{-4}$$\ 	ext{m}^2 is $$placed in a uniform magnetic field $$B at an $$angle of $$60^	ext{o} to $$the field. If the magnetic flux through the area is $$0.90\ 	ext{mWb}$$, what is the magnitude of the magnetic field?

Accepted Answer

$$B = 0.90\ 	ext{mWb} \div (3.0 	imes 10$$^{-4}$$\ 	ext{m}^2 \cos 60^	ext{o}) = 6.0\ 	ext{T}$$

Question 3

Which of the following actions will NOT induce a current in a coil according to the induction experiments shown?

Accepted Answer

Holding both the magnet and coil stationary

Question 4

According to Faraday’s Law, what is the induced emf in a coil with $$N$$ turns when the magnetic flux changes by $$\Delta \Phi_B in $$time $$\Delta t$$?

Accepted Answer

$$\varepsilon = N \frac{\Delta \Phi_B}{\Delta t}$$

Question 5

A circular coil of wire with 500 turns and an average radius of $$4.00\ 	ext{cm} is $$placed at a $$60^	ext{o}$$ angle to a uniform magnetic field. The field changes at a rate of $$-0.200\ 	ext{T/s}. $$What is the magnitude of the resulting induced emf?

Accepted Answer

$$\varepsilon = 500 	imes \pi 	imes (0.04)^2$ 	imes 0.200 	imes \cos 60^	ext{o}$$

Question 6

According to Lenz’s Law, what is the direction of the induced current in a loop when the magnetic flux through the loop is increasing?

Accepted Answer

The induced current creates a magnetic field that opposes the increase in flux

Question 7

A conducting rod of length $$L$$ moves with velocity $$v$$ perpendicular to a uniform magnetic field $$B. $$What is the expression for the motional emf generated across the rod?

Accepted Answer

$$\varepsilon = vBL$$

Question 8

In a slide-wire generator, a rod of length $$0.10\ 	ext{m}$$ moves at $$2.5\ 	ext{m/s} in a $$magnetic field of $$0.60\ 	ext{T}. $$What is the induced emf?

Accepted Answer

$$\varepsilon = 0.10 	imes 2.5 	imes 0.60 = 0.15\ 	ext{V}$$

Question 9

Which medical device uses electromagnetic induction to stimulate neurons in the brain for therapeutic purposes?

Accepted Answer

Transcranial Magnetic Stimulation (TMS)

Question 10

If a circular wire coil is squeezed into a narrow oval while held in a constant magnetic field, how does the magnetic flux through the coil change?

Accepted Answer

The flux decreases because the area decreases

Question 11

A coil with $$N$$ turns is placed in a changing magnetic field. If the field changes at a rate $$\frac{\Delta B}{\Delta t}$$ and the area of the coil is $$A$$, what is the induced emf?

Accepted Answer

$$\varepsilon = N A \frac{\Delta B}{\Delta t}$$

Question 12

Which of the following best describes self-inductance in a coil?

Accepted Answer

A changing current in the coil induces an emf in the same coil

Question 13

The energy stored in a current-carrying inductor is given by which formula?

Accepted Answer

$$U = \frac{1}{2} L I^2$

Question 14

A coil carrying a current of $$200\ 	ext{A} is $$used to store $$1.00\ 	ext{kWh} of $$energy. What inductance is required?

Accepted Answer

$$L = \frac{2U}{I^2$}$$, where $$U = 1.00\ 	ext{kWh} = 3.6 	imes 10^6$\ 	ext{J}$$

Question 15

Which of the following is NOT a real-life application of electromagnetic induction?

Accepted Answer

Ultrasound imaging

Question 16

If the magnetic field through a loop is decreasing, what is the direction of the induced magnetic field according to Lenz’s Law?

Accepted Answer

The induced magnetic field points in the same direction as the original field

Question 17

Which equation gives the energy density of a magnetic field in free space?

Accepted Answer

$$u = \frac{B^2$}{2\mu_0$}$$

Question 18

A utility company uses a transformer to convert high-voltage electric power to lower voltage. Which property of electromagnetic induction is essential for the operation of a transformer?

Accepted Answer

Mutual inductance

Question 19

Which of the following best describes eddy currents?

Accepted Answer

Circulating currents induced in conductors by changing magnetic fields

Electromagnetic Induction: Principles, Laws, and Applications

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