Q: A loudspeaker's voice coil has 60 turns, a diameter of 0.03 m, and is placed in a 0.12 T magnetic field. If the current is 1.8 A, what is the magnitude of the force on the coil? (Assume the wire forms a single loop of length equal to the circumference times the number of turns.)

$$F = (1.8 \ \mathrm{A}) \times 60 \times \pi \times 0.03 \ \mathrm{m} \times 0.12 \ \mathrm{T} = 1.22 \ \mathrm{N}$$

Q: A rod of length $$1.5 \ \mathrm{m}$$ moves at $$3.0 \ \mathrm{m/s}$$ through a $$0.60 \ \mathrm{T}$$ field. If the resistance of the circuit is $$90 \ \Omega$$, what is the current in the circuit?

$$I = \dfrac{v B L}{R} = \dfrac{3.0 \times 0.60 \times 1.5}{90} = 0.03 \ \mathrm{A}$$

Question 1

A solenoid is 0.30 m long and has 6000 turns. If a current of 2.5 A flows through it, what is the magnitude of the magnetic field inside the solenoid? (Use $$\mu_0$ = 4\pi 	imes 10$$^{-7}$$ \ \mathrm{T \cdot m/A})$$

Accepted Answer

$$B = 0.13 \ \mathrm{T}$$

Question 2

A loudspeaker's voice coil has 60 turns, a diameter of 0.03 m, and is placed in a 0.12 T magnetic field. If the current is 1.8 A, what is the magnitude of the force on the coil? (Assume the wire forms a single loop of length equal to the circumference times the number of turns.)

Accepted Answer

$$F = (1.8 \ \mathrm{A}) 	imes 60 	imes \pi 	imes 0.03 \ \mathrm{m} 	imes 0.12 \ \mathrm{T} = 1.22 \ \mathrm{N}$$

Question 3

A galvanometer coil with $$N$$ turns, area $$A$$, and spring constant $$k is $$placed in a magnetic field $$B. If $$the current through the coil is $$I$$, what is the angular displacement $$\Delta \phi of $$the needle for small angles?

Accepted Answer

$$\Delta \phi = \dfrac{N I A B}{k}$$

Question 4

Which of the following best describes the role of the split-ring commutator in a DC motor?

Accepted Answer

It reverses the direction of current in the coil every half turn, ensuring continuous rotation in one direction.

Question 5

A rectangular coil of area $$0.002 \ \mathrm{m}^2$$ with 25 turns is placed in a uniform magnetic field of $$0.40 \ \mathrm{T}$$, perpendicular to the plane of the coil. If the field drops to zero in $$0.05 \ \mathrm{s}$$, what is the average induced emf?

Accepted Answer

$$\mathcal{E} = \dfrac{N \Delta (B A)}{\Delta t} = \dfrac{25 	imes 0.40 	imes 0.002}{0.05} = 0.40 \ \mathrm{V}$$

Question 6

A conducting rod of length $$1.2 \ \mathrm{m}$$ moves at $$4.0 \ \mathrm{m/s}$$ perpendicular to a $$0.50 \ \mathrm{T}$$ magnetic field. What is the induced emf across the ends of the rod?

Accepted Answer

$$\mathcal{E} = v B L = (4.0)(0.50)(1.2) = 2.4 \ \mathrm{V}$$

Question 7

A rod of length $$1.5 \ \mathrm{m}$$ moves at $$3.0 \ \mathrm{m/s}$$ through a $$0.60 \ \mathrm{T}$$ field. If the resistance of the circuit is $$90 \ \Omega$$, what is the current in the circuit?

Accepted Answer

$$I = \dfrac{v B L}{R} = \dfrac{3.0 	imes 0.60 	imes 1.5}{90} = 0.03 \ \mathrm{A}$$

Question 8

Which of the following statements about Lenz’s Law is correct?

Accepted Answer

The induced current always flows in a direction that opposes the change in magnetic flux through the loop.

Question 9

A rectangular coil of area $$A is $$rotated in a uniform magnetic field $$B$$ such that the angle $$\phi$$ between the field and the normal to the coil changes from $$0^\circ to$$ $$90^\circ. $$What happens to the magnetic flux through the coil?

Accepted Answer

It decreases from $$BA to$$ $$0.$$

Question 10

A copper ring is dropped through a region with a constant magnetic field directed into the page. As the ring enters and exits the field, what is the direction of the induced current (viewed from above)?

Accepted Answer

Counterclockwise as it enters, clockwise as it exits.

Question 11

A coil of 15 turns and area $$0.002 \ \mathrm{m}^2 is $$placed perpendicular to a $$0.30 \ \mathrm{T}$$ magnetic field. If the field drops to zero in $$0.10 \ \mathrm{s}$$, what is the magnitude of the average induced emf?

Accepted Answer

$$\mathcal{E} = \dfrac{N \Delta (B A)}{\Delta t} = \dfrac{15 	imes 0.30 	imes 0.002}{0.10} = 0.09 \ \mathrm{V}$$

Question 12

A rod of length $$L$$ moves with velocity $$v$$ perpendicular to a magnetic field $$B. $$Which equation gives the motional emf induced across the rod?

Accepted Answer

$$\mathcal{E} = v B L$$

Question 13

A rectangular coil of area $$0.01 \ \mathrm{m}^2 is $$placed in a $$0.20 \ \mathrm{T}$$ magnetic field. What is the magnetic flux through the coil if the field makes an angle of $$60^\circ$$ with the normal to the coil?

Accepted Answer

$$\Phi = B A \cos \phi = 0.20 	imes 0.01 	imes \cos 60^\circ = 0.001 \ \mathrm{Wb}$$

Question 14

A permanent magnet is moved toward a coil connected to a resistor. According to Lenz’s Law, what is the direction of the induced current in the coil (as viewed from the approaching magnet)?

Accepted Answer

Counterclockwise, creating a magnetic field opposing the approaching magnet.

Question 15

A rod slides down between two vertical copper tracks in a uniform magnetic field directed into the page. If a resistor is connected across the tracks, how does the acceleration of the rod compare to $$g$$?

Accepted Answer

The acceleration is less than $$g$$ due to the upward magnetic force opposing gravity.

Question 16

Which of the following is a correct statement of Faraday’s Law of Electromagnetic Induction?

Accepted Answer

$$\mathcal{E} = -N \dfrac{\Delta \Phi}{\Delta t}$$

Question 17

A coil of 10 turns and area $$0.005 \ \mathrm{m}^2 is $$placed in a $$0.25 \ \mathrm{T}$$ field. If the field is reduced to zero in $$0.20 \ \mathrm{s}$$, what is the average induced emf?

Accepted Answer

$$\mathcal{E} = \dfrac{10 	imes 0.25 	imes 0.005}{0.20} = 0.0625 \ \mathrm{V}$$

Lecture 13

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