Question 1

An airplane with a wingspan of 60.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.400 × l0−⁴ T.If the induced potential between wingtips is 0.600 V,what is the plane's speed? A) 338 m/s B) 375 m/s C) 250 m/s D) 417 m/s

Accepted Answer

C

Question 2

A 10-turn square coil of area 0.036 m² and a 6-turn circular coil are both placed at an angle of 25° to the same changing magnetic field.The voltage induced in each of the coils is the same.What is the area of the circular coil? A) 0.072 m². B) 0.060 m² C) 0.072 m² D) 0.60 m²

Accepted Answer

The voltage induced in a coil is given by the equation: 
V = NABw
Where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and w is the angular frequency of the changing magnetic field. 
Since the voltage induced in both coils is the same, we have: 
N1A1w = N2A2w 
Where N1, A1 are the number of turns and area of the square coil and N2, A2 are the number of turns and area of the circular coil, respectively. 
We know that A1 = 0.036 m2 and N1 = 10. 
Let's assume that the circular coil has an area of A2 m2. 
We also know that the angle between the field and the plane of the coil is 25°. 
The magnetic flux through the circular coil is given by: 
Φ = BA2cos25°
The magnetic flux through the square coil is given by: 
Φ = BA1cos25°
Since both coils have the same induced voltage, we have: 
N1A1w = N2A2w 
We can substitute B from the two flux equations above and solve for A2: 
N1A1cos25° = N2A2cos25° 
10 x 0.036 = 6 x A2 
A2 = 0.06 m2

Question 3

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from 2.0 × 10^-3 T to 3.5 × 10^-3 T in 0.47 s.If the resistance of the loop is 0.31 Ω,what is the current in the loop? A) 7.4 × 10^-4 A B) 5.8 × 10^-4 A C) 2.9 × 10^-3 A D) 5.8 × 10^-3 A

Accepted Answer

C

Question 4

A coil in a magnetic field encloses a flux of 0.256 T·m² when the angle between the normal to the coil and the direction of the magnetic field is 70.0°.What flux would go through the coil if the angle were changed to 30.0°? A) 0.648 T·m² B) 0.573 T·m² C) 0.114 T·m² D) 0.198 T·m²

Accepted Answer

We can use the formula for flux through a coil in a magnetic field: Φ = B*A*cos(θ) where Φ is the flux, B is the magnetic field, A is the area enclosed by the coil, and θ is the angle between the normal to the coil and the direction of the magnetic field. We can rearrange the formula to solve for the new flux when the angle is changed to 30.0°: Φ' = B*A*cos(30.0°) = (0.256 T) * (m^2) * cos(30.0°) = 0.648 T·m² Therefore, the answer is A.

Question 5

A circular loop of wire has its radius doubled in time Ät.A uniform magnetic field is at an angle of 60^° to the plane of the coil,and the magnetic field halves its intensity in the same time interval Ät.During this interval,what happens to the flux through the coil? A) It decreases. B) It remains the same. C) It increases. D) More information is needed to make this conclusion.

Accepted Answer

The magnetic flux is proportional to the product of the magnetic field strength, the area of the loop, and the cosine of the angle between the field and the normal to the loop. Doubling the radius increases the area by a factor of four, while halving the magnetic field strength reduces the flux by a factor of two. Overall, the flux increases by a factor of two.

Question 6

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from 2.0 × 10^-3 T to 3.5 × 10^-3 T in 0.47 s.What is the induced emf in the wire? A) 9.0 ×10^-4 V B) 2.3 ×10^-4 V C) 1.8 ×10^-3 V D) 1.8 ×10^-4 V

Accepted Answer

The answer of The magnetic field inside a circular loop...

Question 7

A loop of area 0.250 m² is in a uniform 0.0200-T magnetic field.If the flux through the loop is 3.21 × 10^-3 T·m²,what angle does the normal to the plane of the loop make with the direction of the magnetic field? A) 40.0° B) 37.5° C) 50.0° D) This is not possible.

Accepted Answer

The answer of A loop of area 0.250 m² is...

Question 8

A coil is placed in a magnetic field and has a flux Φ_B through it.The coil is stressed so that its area reduces to 60% of its original value.If the plane of the coil stays the same and the flux through it remains the same,how must the magnetic field change? A) It must increase by 60%. B) It must increase by 120%. C) It must decrease by 40%. D) It must increase by 67%.

Accepted Answer

The magnetic flux Φ is given by Φ = B * A, where B is the magnetic field and A is the area. If the area decreases to 60% of its original value, the magnetic field must increase to maintain the same flux. The increase required is 1/0.6 - 1 = 0.67 or 67%.

Question 9

A flat coil of wire consisting of 20 turns,each with an area of 80 cm²,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s.If the coil has a total resistance of 0.40 Ω,what is the magnitude of the induced current? A) 500 mA B) 70 mA C) 140 mA D) 800 mA

Accepted Answer

The answer of A flat coil of wire consisting of...

Question 10

The self-inductance of a solenoid increases under which of the following conditions?
A) Only the cross sectional area is decreased.
B) Only the number of coils per unit length is decreased.
C) Only the number of coils is increased.
D) Only the solenoid length is increased.

Accepted Answer

The self-inductance of a solenoid is directly proportional to the square of the number of coils. Increasing the number of coils increases the self-inductance.

Question 11

A large jetliner with a wingspan of 40 m flies horizontally and due north at a speed of 300 m/s in a region where the magnetic field of the earth is 51 µT directed 24.1° below the horizontal.What is the magnitude of the induced emf between the ends of the wing?
A) 350 mV
B) 750 mV
C) 550 mV
D) 250 mV

Accepted Answer

The answer of A large jetliner with a wingspan of...

Question 12

The current in a coil with a self-inductance of 1.5 mH increases from 0 to 2.0 A in a tenth of a second.What is the induced emf in the coil?
A) 15 mV
B) 0.30 V
C) 0.10 V
D) 30 mV

Accepted Answer

We can use the formula for induced emf in a coil:

emf = -L(dI/dt)

Where L is the self-inductance, I is the current, and dt is the change in time.

Substituting the values, we get:

emf = -(1.5 mH)(2.0 A/0.1 s) = -30 mV

Since the emf is induced in the opposite direction to the change in current, we take the absolute value to get the final answer:

emf = 30 mV, which is option D.

Question 13

A coil is placed in a changing magnetic field and an emf is induced.What happens to the induced emf if the rate of change of magnetic field doubles?
A) The emf quadruples.
B) The emf increases by a factor of 16.
C) There is no change.
D) The emf doubles.

Accepted Answer

According to Faraday's Law of Electromagnetic Induction, the magnitude of the induced emf is directly proportional to the rate of change of the magnetic field. Therefore, if the rate of change of magnetic field doubles, the induced emf also doubles.

Question 14

A uniform 1.5-T magnetic field passes perpendicularly through the plane of a wire loop 0.30 m² in area.What flux passes through the loop? A) 0.135 T⋅m² B) 5.0 T⋅m² C) 0.45 T⋅m² D) 0.25 T⋅m²

Accepted Answer

The flux passing through the loop is given by the formula:
Φ = B A cosθ

where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop.

Here, the magnetic field is perpendicular to the loop so θ = 0° and cosθ = 1. Thus, the flux passing through the loop is:

Φ = (1.5 T)(0.30 m2) = 0.45 T⋅m2

Therefore, the best choice is C.

Question 15

A planar loop consisting of four turns of wire,each of which encloses 250 cm²,is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms.What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω? A) 48 mA B) 0.24 mA C) 12 mA D) 60 mA

Accepted Answer

The answer of A planar loop consisting of four turns...

Question 16

A uniform 4.5-T magnetic field passes through the plane of a wire loop 0.20 m² in area.What flux passes through the loop when the direction of the 4.5-T field is at a 30° angle to the normal of the loop plane? A) 0.39 T⋅m² B) 5.0 T⋅m² C) 0.78 T⋅m² D) 0.225 T⋅m²

Accepted Answer

The flux passing through the wire loop can be calculated using the formula:

Φ = B*A*cos(θ)

where Φ is the flux, B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop.

In this case, B = 4.5 T, A = 0.20 m^2, and θ = 30°. Using the above formula, we get:

Φ = 4.5 T * 0.20 m^2 * cos(30°) = 0.78 T⋅m^2

Therefore, the answer is (C) 0.78 T⋅m^2.

Question 17

A coil with a self-inductance of 0.75 mH experiences a constant current buildup from zero to 15 A in 0.25 s.What is the induced emf during this interval?
A) 0.045 V
B) 0.47 V
C) 0.030 V
D) 0.019 V

Accepted Answer

The induced emf (ε) in a coil is given by the formula ε = -L * (ΔI/Δt), where L is the self-inductance, ΔI is the change in current, and Δt is the time interval. Substituting the given values: ε = -0.75 mH * (15 A / 0.25 s) = -0.75 * 10^-3 H * 60 A/s = -0.045 V. The negative sign indicates the direction of the induced emf, but the magnitude is 0.045 V.

Question 18

A 0.200-m wire is moved parallel to a 0.500-T magnetic field at a speed of 6.00 m/s.What emf is induced across the ends of the wire?
A) 1.00 V
B) 0.600 V
C) 2.25 V
D) zero

Accepted Answer

When a wire moves parallel to a magnetic field, no emf is induced because the motion does not cut across the magnetic field lines.

Question 19

Three loops of wire,one circular,one rectangular,and one square,are made from identical lengths of wire.If the loops are in the same increasing magnetic field perpendicular to the plane of the coils,which loop has the least induced emf?
A) the square one
B) the rectangular one
C) the circular one
D) All three would have the same emf induced.

Accepted Answer

The answer of Three loops of wire,one circular,one rectangular,and one...

Question 20

A square coil,enclosing an area with sides 3.0 cm long,is wrapped with 2500 turns of wire.A uniform magnetic field perpendicular to its plane is turned on and increases to 0.12 T during an interval of 1.0 s.What average voltage is induced in the coil?
A) 2.5 V
B) 0.27 V
C) 1.2 V
D) 0.12 V

Accepted Answer

The average induced voltage (emf) can be calculated using Faraday's law of electromagnetic induction: emf = -N * (ΔΦ/Δt), where N is the number of turns, ΔΦ is the change in magnetic flux, and Δt is the time interval. The area A of the coil is (0.03 m)^2 = 0.0009 m². The change in magnetic flux ΔΦ = B * A = 0.12 T * 0.0009 m² = 0.000108 Wb. Therefore, emf = -2500 * (0.000108 Wb / 1 s) = 0.27 V.

Quiz 21: Alternating-Current Circuits and Electromagnetic Waves: Part A

An airplane with a wingspan of 60.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.400 × l0−4 T.If the induced potential between wingtips is 0.600 V,what is the plane's speed?

A 10-turn square coil of area 0.036 m2 and a 6-turn circular coil are both placed at an angle of 25° to the same changing magnetic field.The voltage induced in each of the coils is the same.What is the area of the circular coil?

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from 2.0 × 10-3 T to 3.5 × 10-3 T in 0.47 s.If the resistance of the loop is 0.31 Ω,what is the current in the loop?

A coil in a magnetic field encloses a flux of 0.256 T·m2 when the angle between the normal to the coil and the direction of the magnetic field is 70.0°.What flux would go through the coil if the angle were changed to 30.0°?

A circular loop of wire has its radius doubled in time Ät.A uniform magnetic field is at an angle of 60° to the plane of the coil,and the magnetic field halves its intensity in the same time interval Ät.During this interval,what happens to the flux through the coil?

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from 2.0 × 10-3 T to 3.5 × 10-3 T in 0.47 s.What is the induced emf in the wire?

A loop of area 0.250 m2 is in a uniform 0.0200-T magnetic field.If the flux through the loop is 3.21 × 10-3 T·m2,what angle does the normal to the plane of the loop make with the direction of the magnetic field?

A coil is placed in a magnetic field and has a flux ΦB through it.The coil is stressed so that its area reduces to 60% of its original value.If the plane of the coil stays the same and the flux through it remains the same,how must the magnetic field change?

A flat coil of wire consisting of 20 turns,each with an area of 80 cm2,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s.If the coil has a total resistance of 0.40 Ω,what is the magnitude of the induced current?

The self-inductance of a solenoid increases under which of the following conditions?

A large jetliner with a wingspan of 40 m flies horizontally and due north at a speed of 300 m/s in a region where the magnetic field of the earth is 51 µT directed 24.1° below the horizontal.What is the magnitude of the induced emf between the ends of the wing?

The current in a coil with a self-inductance of 1.5 mH increases from 0 to 2.0 A in a tenth of a second.What is the induced emf in the coil?

A coil is placed in a changing magnetic field and an emf is induced.What happens to the induced emf if the rate of change of magnetic field doubles?

A uniform 1.5-T magnetic field passes perpendicularly through the plane of a wire loop 0.30 m2 in area.What flux passes through the loop?

A planar loop consisting of four turns of wire,each of which encloses 250 cm2,is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms.What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω?

A uniform 4.5-T magnetic field passes through the plane of a wire loop 0.20 m2 in area.What flux passes through the loop when the direction of the 4.5-T field is at a 30° angle to the normal of the loop plane?

A coil with a self-inductance of 0.75 mH experiences a constant current buildup from zero to 15 A in 0.25 s.What is the induced emf during this interval?

A 0.200-m wire is moved parallel to a 0.500-T magnetic field at a speed of 6.00 m/s.What emf is induced across the ends of the wire?

Three loops of wire,one circular,one rectangular,and one square,are made from identical lengths of wire.If the loops are in the same increasing magnetic field perpendicular to the plane of the coils,which loop has the least induced emf?

A square coil,enclosing an area with sides 3.0 cm long,is wrapped with 2500 turns of wire.A uniform magnetic field perpendicular to its plane is turned on and increases to 0.12 T during an interval of 1.0 s.What average voltage is induced in the coil?

An airplane with a wingspan of 60.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.400 × l0−⁴ T.If the induced potential between wingtips is 0.600 V,what is the plane's speed?

A 10-turn square coil of area 0.036 m² and a 6-turn circular coil are both placed at an angle of 25° to the same changing magnetic field.The voltage induced in each of the coils is the same.What is the area of the circular coil?

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from 2.0 × 10^-3 T to 3.5 × 10^-3 T in 0.47 s.If the resistance of the loop is 0.31 Ω,what is the current in the loop?

A coil in a magnetic field encloses a flux of 0.256 T·m² when the angle between the normal to the coil and the direction of the magnetic field is 70.0°.What flux would go through the coil if the angle were changed to 30.0°?

A circular loop of wire has its radius doubled in time Ät.A uniform magnetic field is at an angle of 60^° to the plane of the coil,and the magnetic field halves its intensity in the same time interval Ät.During this interval,what happens to the flux through the coil?

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from 2.0 × 10^-3 T to 3.5 × 10^-3 T in 0.47 s.What is the induced emf in the wire?

A loop of area 0.250 m² is in a uniform 0.0200-T magnetic field.If the flux through the loop is 3.21 × 10^-3 T·m²,what angle does the normal to the plane of the loop make with the direction of the magnetic field?

A coil is placed in a magnetic field and has a flux Φ_B through it.The coil is stressed so that its area reduces to 60% of its original value.If the plane of the coil stays the same and the flux through it remains the same,how must the magnetic field change?

A flat coil of wire consisting of 20 turns,each with an area of 80 cm²,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s.If the coil has a total resistance of 0.40 Ω,what is the magnitude of the induced current?

A uniform 1.5-T magnetic field passes perpendicularly through the plane of a wire loop 0.30 m² in area.What flux passes through the loop?

A planar loop consisting of four turns of wire,each of which encloses 250 cm²,is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms.What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω?

A uniform 4.5-T magnetic field passes through the plane of a wire loop 0.20 m² in area.What flux passes through the loop when the direction of the 4.5-T field is at a 30° angle to the normal of the loop plane?