Physics II, Test II: CH 21, 22, 23, 24, 25 (How to Solve)

A proton, starting from rest, accelerates through a potential difference of 1.0 kV and then moves into a magnetic field of 0.040 T at a right angle to the field. What is the radius of the proton's resulting orbit? (e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg)

0.11 m

A proton having a speed of 3.0 × 106 m/s in a direction perpendicular to a uniform magnetic field moves in a circle of radius 0.20 m within the field. What is the magnitude of the magnetic field? (e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg)

0.16 T

An electron moving perpendicular to a uniform magnetic field of 0.22 T moves in a circle with a speed of 1.5 × 107 m/s. What is the radius of the circle? (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31kg)

0.39 mm

The secondary coil of an ideal neon sign transformer provides 7500 V at 10.0 mA. The primary coil operates on 120 V. What current does the primary draw?

0.625 A

A straight wire carries a current of 10 A at an angle of 30° with respect to the direction of a uniform 0.30-T magnetic field. Find the magnitude of the magnetic force on a 0.50-m length of the wire.

0.75 N

A glass plate having an index of refraction is 1.66 is immersed in a certain alcohol. The surface of the glass is inclined at an angle of 44° with the vertical. When a horizontal ray in the glass strikes the interface, you observe that it is at the critical angle. What is the index of refraction of the alcohol?

1.15

A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0°. It is observed that the reflected and refracted beams form an angle of 90.0°. What is the index of refraction of this material?

1.48

A round flat conducting loop is placed perpendicular to a uniform 0.50 T magnetic field. If the area of the loop increases at a rate of 3.0 × 10-3 m2/s, what is the induced emf in the loop?

1.5 mV

Light having a speed in vacuum of 3.0 × 108 m/s enters a liquid of refractive index 2.0. In this liquid, its speed will be

1.5 x 10^8 m/s

A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the highest frequency associated with this portion of the spectrum? (c = 3.00 × 108 m/s)

1.50 x 10^15 Hz

An electron moves with a speed of 5.0 × 104 m/s perpendicular to a uniform magnetic field of magnitude 0.20 T. What is the magnitude of the magnetic force on the electron? (e = 1.60 × 10-19 C)

1.6 × 10-15 N

A proton moving eastward with a velocity of 5.0 km/s enters a magnetic field of 0.20 T pointing northward. What are the magnitude and direction of the force that the magnetic field exerts on the proton? (e = 1.60 × 10-19 C)

1.6 × 10-16 N upwards

A circular coil with 600 turns has a radius of 15 cm. The coil is rotating about an axis perpendicular to a magnetic field of 0.020 T. If the maximum induced emf in the coil is 1.6 V, at what angular frequency is the coil rotating?

1.9 rad/s

An electron moves with a speed of 3.0 × 104 m/s perpendicular to a uniform magnetic field of 0.40 T. What is the magnitude of the magnetic force on the electron? (e = 1.60 × 10-19 C)

1.9 × 10-15 N

The amplitude of the electric field for a certain type of electromagnetic wave is 570 N/C. What is the amplitude of the magnetic field for that wave? (c = 3.00 × 108 m/s)

1.90 µT

The coil of an ac generator has 50 loops and a cross-sectional area of 0.25 m2. What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of 4.0 rad/s in a 2.0-T magnetic field?

100 V

A glass plate with an index of refraction is 1.57 is immersed in an oil having a refractive index of 1.40. The surface of the glass is inclined at an angle of 54° with the vertical. A horizontal light ray in the glass strikes the interface. What is the angle that the refracted ray, in the oil, makes with the horizontal?

11°

A current of 2.0 A in the 100-turn primary of an ideal transformer causes 14 A to flow in the secondary. How many turns are in the secondary?

14

What is the frequency of 20-mm microwaves? (c = 3.0 × 108 m/s)

15 GHz

An ideal step-up transformer doubles a primary voltage of 110 V. What is the ratio of the number of turns in its primary coil to the number of turns in the secondary coil?

1:2

A beam of light traveling in air strikes a slab of transparent material. The incident beam makes an angle of 40° with the normal, and the refracted beam make an angle of 26° with the normal. What is the speed of light in the transparent material? (c = 3.0 × 108 m/s)

2.0 x 10^8 m/s

An electron moving perpendicular to a uniform magnetic field of 3.2 × 10-2 T moves in a circle of radius 0.40 cm. How fast is this electron moving? (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31kg)

2.2 × 107 m/s

The area of a rectangular loop of wire is 3.6 × 10-3 m2. The loop is placed in a uniform magnetic field that changes steadily from 0.20 T to 1.4 T in 1.6 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 × 10-3 V

A radio station broadcasts at a frequency of 80 MHz. How far from the transmitter will this signal travel in 67 ms? (c = 3.0 × 108 m/s)

20 × 10^6 m

A beam of light in air enters a glass slab with an index of refraction of 1.40 at an angle of incidence of 30.0°. What is the angle of refraction?

20.9°

A 7.55 × 1014 Hz electromagnetic wave travels in carbon tetrachloride with a speed of 2.05 ×108 m/s. What is the wavelength of the wave in this material?

272 nm

An ac generator contains 80 flat rectangular loops of wire, each of which is 12 cm long and 8 cm wide. The loops rotate at 1200 rpm about an axis through the center and parallel to the long side. If the magnetic field in which the loop rotates is uniform, has magnitude 0.30 T, and is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator?

29 V

A light source radiates 60.0 W of single-wavelength sinusoidal light uniformly in all directions. What is the average intensity of the light from this bulb at a distance of 0.400 m from the bulb?

29.8 W/m^2

A straight 1.0-m long wire is carrying a current. The wire is placed perpendicular to a magnetic field of strength 0.20 T. If the wire experiences a force of 0.60 N, what is the current in the wire?

3.0 A

What is the wavelength used by a radio station that broadcasts at a frequency of 920 kHz? (c = 3.00 × 108 m/s)

326 m

An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. A light ray from the air above enters the oil at 45° with the normal and then goes into the water. What is the angle of refraction of this ray in the water? The index of refraction for the oil is 1.15, and for water it is 1.33.

32°

A laser beam takes 24 ms to travel from a rocket to the reflective surface of a planet and back to the rocket. How far is the rocket from this planet's surface? (c = 3.0 × 108 m/s)

3600 km

About 1350 W/m2 of electromagnetic energy reaches the upper atmosphere of the earth from the sun, which is 1.5 × 10^11 m away. Use this information to estimate the average power output of the sun.

4 × 10^26 W

A certain electromagnetic field traveling in vacuum has a maximum electric field of 1200 V/m. What is the maximum magnetic field of this wave? (c = 3.0 × 108 m/s)

4.0 x 10^-6 T

A proton travels at a speed of 5.0 × 107 m/s through a 1.0-T magnetic field. What is the magnitude of the magnetic force on the proton if the angle between the proton's velocity and the magnetic field vector is 30°? (e = 1.60 × 10-19 C)

4.0 × 10-12 N

A constant uniform magnetic field of 0.50 T is applied at right angles to the plane of a flat rectangular loop of area 3.0 × 10-3 m2. If the area of this loop changes steadily from its original value to a new value of 1.6 × 10-3 m2 in 1.6 s, what is the emf induced in the loop?

4.4 x 10-4 V

Lucite has an index of refraction of 1.50. What is its critical angle if it is in air?

41.8°

In an ideal transformer, how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns?

458

A light ray in air strikes a glass plate whose index of refraction is 1.42. Some of the light reflects off the surface of the plate, but most of it enters the glass. If the angle of refraction is one-half the angle of reflection, the angle of refraction is closest to which one of the following angles?

45°

The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is 120 V, what voltage is present in its secondary coil?

480 V

A scuba diver is 1.2 m beneath the surface of a still pond of water. At what angle relative to the normal at the surface must the diver shine a beam of light toward the surface in order for a person on a distant bank to be able to see it? The index of refraction for water is 1.33.

48°

An electron is accelerated from rest through a potential difference of 3.75 kV. It enters a region where a uniform 4.0-mT magnetic field is perpendicular to the velocity of the electron. Calculate the radius of the path this electron will follow in the magnetic field. (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg)

5.2 cm

A beam of light in water (of refractive index of 1.33) enters a glass slab (of refractive index 1.50) at an angle of incidence of 60.0°. What is the angle of refraction in the glass?

50.2°

The wavelength of an electromagnetic wave is 600 nm. What is its frequency? (c = 3.0 × 108 m/s)

500 × 10^12 Hz

Light enters a substance from air at 30.0° to the normal. It continues within the substance at 23.0° to the normal. What is the critical angle for this substance when it is surrounded by air?

51.4°

How far does a beam of light travel in 2.0 ms? (c = 3.0 × 108 m/s)

6.0 × 10^5 m

A flat rectangular coil with dimensions of 8.0 cm × 10 cm is dropped from a zero magnetic field position into a 1.4-T magnetic field in 0.10 s. The coil has 60 turns and is perpendicular to the magnetic field. What is the average induced emf in the coil as a result of this action?

6.7 V

A proton is projected with a velocity of 7.0 km/s into a magnetic field of 0.60 T perpendicular to the motion of the proton. What is the magnitude of the magnetic force that acts on the proton? (e = 1.60 × 10-19 C)

6.7 × 10-16 N

A flashlight beam makes an angle of 60° with the plane of the surface of a calm lake before it enters the water. In the water what angle does the beam make with the plane of the surface? The index of refraction of water is 1.33.

68°

You are designing an ac generator with a maximum emf of 8.0 V. If the generator coil has 200 turns, each with a cross-sectional area of 0.030 m2, what should be the frequency of the generator in a magnetic field of 0.030 T?

7.1 Hz

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 A, what is the current in its primary coil?

8 A

The primary coil of an ideal transformer has 600 turns and its secondary coil has 150 turns. If the current in the primary coil is 2 A, what is the current in its secondary coil?

8 A

A flat square coil of wire with 15 turns and an area of 0.40 m2 is placed with the plane of its area parallel to a magnetic field of 0.75 T. The coil is flipped so its plane is perpendicular to the magnetic field in a time of 0.050 s. What is the magnitude of the average induced emf in the coil?

90 V

How far does a beam of light travel through space in one 365-day year? (c = 3.0 × 108 m/s)

95 x 10^14 m

Three light bulbs, A, B, and C, have electrical ratings as follows: Bulb A: 96.0 W, 1.70 A Bulb B: 80.0 V, 205 W Bulb C: 120 V, 0.400 A These three bulbs are connected in a circuit across a 150-V voltage power source, as shown in the figure. Assume that the filament resistances of the light bulbs are constant and independent of operating conditions. What is the equivalent resistance of this combination of bulbs between the terminals of the power source?

Bulb A: P = I^2 • R R = P / I^2 P: 96.0 W I: 1.70 A R = 96 / 1.7^2 R = 33.22 Ohms Bulb B: P = V^2 / R R = V^2 / P V: 80.0 V P: 205 W R = 80^2 / 205 R = 31.22 Ohms Bulb C: V = I • R R = V / I V: 120 V I: 0.400 A R = 120 / 0.4 R = 300 Ohms Resistors in a Parallel Series: Rt = 1 / ((1 / R1) + (1 / R2) + (1 / R3)...) 1 / R1: (1 / 31.22 Ohms) = 0.032 / Ohms 1 / R2: (1 / 300 Ohms) = 0.003 / Ohms Rt = 1 / (2.65 + 0.003) Rt = 28.28 Ohms Resistors in a Series: Rt = R1 + R2 + R3... R1: 33.22 Ohms R2: 28.28 Ohms Rt = 33.22 + 28.28 Rt = 61.49 ≈ 61.5 Ohms 61.5 Ohms

A straight wire that is 0.60 m and carrying a current of 2.0 A is placed at an angle with respect to the magnetic field of strength 0.30 T. If the wire experiences a force of magnitude 0.18 N, what angle does the wire make with respect to the magnetic field

F = BLIsinθ B: 0.30 T L: 0.60 m I: 2.0 A F: 0.18 N 0.18 = 0.30 • 0.60 • 2 • sinθ 0.5 = sinθ sin^-1 (0.5) = θ = 30° 30°

A proton moving with a velocity of 4.0 × 10^4 m/s along the +y-axis enters a magnetic field of 0.20 T directed towards the -x-axis. What is the magnitude of the magnetic force acting on the proton? (e = 1.60 × 10^-19 C)

F = q x V x B q: 1.60 • 10^-19 C V: 4.0 • 10^4 m/s B: 0.20 T F = (1.6 • 10^-19) x (4 • 10^4) x (0.20) F = 1.28 • 10^-15 ≈ 1.3 • 10^-15 N 1.3 × 10^-15 N

A proton moving with a velocity of 4.0 × 10^4 m/s enters a magnetic field of 0.20 T. If the angle between the velocity of the proton and the direction of the magnetic field is 60°, what is the magnitude of the magnetic force on the proton? (e = 1.60 × 10-19 C)

F = qvBsinθ q: 1.60 • 10^-19 C v: 4.0 • 10^4 m/s B: 0.20 T θ: 60° F = (1.60 • 10^-19) x (4.0 • 10^4) x 0.20 x sin (60) F = 1.108 • 10^-15 N ≈ 1.1 • 10^-15 N 1.1 × 10-15 N

A doubly charged ion with speed 6.9 × 10^6 m/s enters a uniform 0.80-T magnetic field, traveling perpendicular to the field. Once in the field, it moves in a circular arc of radius 30 cm. What is the mass of this ion? (e = 1.60 × 10-19 C)

Fm = Fc Bqv = mv^2 / r m = Bqr / v B: 0.80 T q: 1.60 • 10^-19 C (double charge ion) multiply by 2 r: 30 cm = 30 • 10^-2 m v: 6.9 • 10^6 m/s m = ( 0.80 x (2 x (1.6 • 10^-19)) x ( 30 • 10^-2) ) / (6.9 • 10^6) m = 1.1 • 10^-26 = 11 • 10^-27 11 × 10-27 kg

The following three appliances are connected in parallel across an ideal 120-V dc power source: 1200-W toaster, 650-W coffee pot, and 600-W microwave. If all were operated at the same time what total current would they draw from the source?

I = P / V P: 1200 W + 650 W + 600 W = 2450 W V: 120 V I = 2450 / 120 I = 20.42 A ≈ 20 A 20 A

A certain 20-A circuit breaker trips when the current in it equals 20 A. What is the maximum number of 100-W light bulbs you can connect in parallel in an ideal 120-V dc circuit without tripping this circuit breaker?

P = I • V P = (I/n) • V n = I / (P / V) I: 20 A P: 100 W V: 120 V n = 20 / (100 / 120) n = 24 24 light bulbs will trip it so maximum # is 23 23 light bulbs

In the circuit below, R1=100 ohms, R2=300 ohms and Rn=50 ohms. What is the total resistance?

Resistors in a Parallel Series: Rt = 1 / ((1 / R1) + (1 / R2) + (1 / R3)...) 1 / R1 = (1 / 100 Ohms) = 0.01 / Ohms 1 / R2 = (1 / 300 Ohms) = 0.003 / Ohms 1 / R3 = (1 / 50 Ohms) = 0.02 / Ohms Rt = 1 / (0.01 + 0.003 + 0.02) Rt = 30.3 ≈ 28.6 Ohms 28.6 Ohms

In the circuit below, what is the total resistance?

Resistors in a Parallel Series: Rt = 1 / ((1 / R1) + (1 / R2) + (1 / R3)...) 1 / R1: (1 / 12 Ohms) = 0.083 / Ohms 1 / R2: (1 / 6 Ohms) = 0.167 / Ohms Rt = 1 / (0.083 + 0.167) Rt = 4 Ohms Resistors in a Series: Rt = R1 + R2 + R3... R1: 4 Ohms R2: 4 Ohms Rt = 4 + 4 Rt = 8 Ohms 8 Ohms

What is the total resistance in the circuit below?

Resistors in a Parallel Series: Rt = 1 / ((1 / R1) + (1 / R2) + (1 / R3)...) 1 / R1: (1 / 24 Ohms) = 0.0417 / Ohms 1 / R2: (1 / 8 Ohms) = 0.125 / Ohms Rt = 1 / (0.0417 + 0.125) Rt = 5.99 Ohms Resistors in a Series: Rt = R1 + R2 + R3... R1: 4 Ohms R2: 5.99 Ohms Rt = 4 + 5.99 Rt = 9.99 ≈ 10 Ohms 10 Ohms

What is the total current in the circuit below?

Resistors in a Parallel Series: Rt = 1 / ((1 / R1) + (1 / R2) + (1 / R3)...) 1 / R1: (1 / 24 Ohms) = 0.0417 / Ohms 1 / R2: (1 / 8 Ohms) = 0.125 / Ohms Rt = 1 / (0.0417 + 0.125) Rt = 5.99 Ohms Resistors in a Series: Rt = R1 + R2 + R3... R1: 4 Ohms R2: 5.99 Ohms Rt = 4 + 5.99 Rt = 9.99 ≈ 10 Ohms V = I • R I = V / R V: 30 V R: 10 Ohms I = 30 / 10 I = 3 A 3 Amps

In the circuit below, if R1=100 ohms and R2=200 ohms and the total resistance is 54.5 ohms, what is the value of Rn?

Resistors in a Parallel Series: Rt = 1 / ((1 / R1) + (1 / R2) + (1 / R3)...) R3 = 1 / ((1 / Rt) - (1 / R1) - (1 / R2)) 1 / Rt: (1 / 54.5 Ohms) = 0.018 / Ohms 1 / R1: (1 / 100 Ohms) = 0.01 Ohms 1 / R2: (1 / 200 Ohms) = 0.005 Ohms R3 = 1 / (0.018 - 0.01 - 0.005) R3 = 333.33 Ohms ≈ 300 Ohms 300 Ohms

If the source voltage in the circuit below is 10 v, and the three resistors are 100, 200, and 300 ohms. What is the current?

Resistors in a Series: Rt = R1 + R2 + R3... R1: 100 Ohms R2: 200 Ohms R3: 300 Ohms Rt = 100 + 200 + 300 Rt = 600 Ohms V = I • R I = V / R V: 10 V R: 600 Ohms I = 10 / 600 I = 0.0167 = 0.017 A 0.017 A

An ideal 100-V dc battery is applied across a series combination of four resistors having resistances of 20 ohms, 40 ohms, 60 ohms, and 80 ohms. What is the potential difference across the 40-ohm resistor?

Resistors in a Series: Rt = R1 + R2 + R3... R1: 20 Ohms R2: 40 Ohms R3: 60 Ohms R4: 80 Ohms Rt = 20 + 40 + 60 + 80 Rt = 200 Ohms V = I • R I = V / R V: 100 V R: 200 Ohms I = 100 / 200 I = 0.50 V V = I • R (for 40 Ohms Resistor) I: 0.50 V R: 40 Ohms V = 0.50 • 40 V = 20 V 20 V

In the circuit below, the three resistors are all 300 ohms. What is the total resistance?

Resistors in a Series: Rt = R1 + R2 + R3... R1: 300 Ohms R2: 300 Ohms R3: 300 Ohms Rt = 300 + 300 + 300 Rt = 900 Ohms 900 Ohms

A 2.0-microF capacitor that is initially uncharged is charged through a 50-kilo-ohm resistor. How long does it take for the capacitor to reach 90% of its full charge?

q = q0 [ 1 - e^(-t/RC) ] q: 0.90 q0: N/A R: 50 kOhms = 50,000 Ohms C: 2.0 microF = 2 • 10^-6 0.90 = 1 - e^(-t / (50000 • (2 • 10^-6)) 0.1 = e^(-t / (50000) • (2 • 10^-6)) -t / 0.1 = ln 0.1 -t / 0.1 = -2.30 -t = -0.23 t = 0.23 s 0.23 s