Question 1

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T • m/A) A) 7.3 × 10^-5 J/m³ B) 3.7 × 10^-5 J/m³ C) 3.6 × 10^-4 J/m³ D) 1.2 × 10^-4 J/m³ E) The density cannot be determined without knowing the volume.

Accepted Answer

The energy density $u$ in a magnetic field is given by the formula $u = \frac{B^2}{2\mu_0}$, where $B$ is the magnetic field strength and $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$). The magnetic field $B$ around a long straight wire is given by $B = \frac{\mu_0 I}{2\pi r}$, where $I$ is the current and $r$ is the distance from the wire. Substituting $I = 12 \, \text{A}$ and $r = 0.25 \, \text{m}$, and then calculating $u$, results in the energy density value corresponding to choice B.

Question 2

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T • m/A) A) 4.19 nH B) 4.19 pH C) 4.19 µH D) 4.19 mH E) 4.19 H

Accepted Answer

First, we need to use the formula for the self-inductance of a solenoid:

L = μ0n2Aℓ / l

where μ0 is the permeability of free space (given as 4π × 10-7 T·m/A), n is the number of turns per unit length (in this case, it's simply 100/ℓ), A is the cross-sectional area, and ℓ is the length of the solenoid.

Plugging in the given values, we get:

n = 100 / 0.30 = 333.33 turns/m
A = 1.00 × 10-4 m2
ℓ = 0.30 m

L = (4π × 10-7 T·m/A) * (333.33 turns/m)2 * (1.00 × 10-4 m2) * 0.30 m / 1 m

L = 4.19 µH

Therefore, the answer is C, 4.19 µH.

Question 3

For a long ideal solenoid having a circular cross-section,the magnetic field strength within the solenoid is given by the equation B(t)= 5.0t T,where t is time in seconds.If the induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid,find the radius of the solenoid.
A) 0.30 m
B) 77 m
C) 0.94 m
D) 9.0 m

Accepted Answer

We know that outside the solenoid, the magnetic field is zero due to the absence of magnetic monopoles. Therefore, any induced electric field must be due to a changing magnetic flux through a closed loop. We can find the induced electric field by applying Faraday's law:
$$\oint \vec{E}\cdot d\vec{l}=-\frac{d\phi_B}{dt}$$
Since the electric field is radial, we can integrate over a circular path of radius 2.0 m to get:
$$E(2\pi r) = -\frac{d\phi_B}{dt}$$
where $\phi_B$ is the magnetic flux through the circular path. The magnetic field is given by $B(t)=5.0t$ T, so the magnetic flux is:
$$\phi_B = \int B(t) dA = B(t) \pi r^2$$
Taking the time derivative, we get:
$$\frac{d\phi_B}{dt} = 5.0\pi r^2$$
Substituting into Faraday's law and solving for the radius, we get:
$$E(2\pi r) = -5.0\pi r^2$$
$$r = \sqrt{\frac{-E}{10\pi}} = \boxed{0.94\ m}$$
Therefore, the best choice is C.

Question 4

The coil in a 60-Hz ac generator has 125 turns,each having an area of 3.0 × 10^-2 m² and is rotated in a uniform 0.12-T magnetic field.What is the peak output voltage of this generator? A) 170 V B) 120 V C) 200 V D) 110 V E) 220 V

Accepted Answer

The answer of The coil in a 60-Hz ac generator...

Question 5

You are designing a generator to have a maximum emf of 8.0 V. If the generator coil has 200 turns and a cross-sectional area of 0.030 m²,what should be the frequency of the generator in a uniform magnetic field of 0.030 T? A) 7.1 Hz B) 7.5 Hz C) 8.0 Hz D) 22 Hz E) 44 Hz

Accepted Answer

The maximum emf (E_max) generated by a coil in a magnetic field can be calculated using the formula: E_max = NABωsin(θ), where N is the number of turns, A is the area, B is the magnetic field strength, ω is the angular frequency (ω = 2πf, where f is the frequency), and θ is the angle between the magnetic field and the normal to the coil. Since the maximum emf occurs when sin(θ) = 1, the equation simplifies to E_max = NABω. Solving for frequency (f), we get f = E_max / (2πNAB).Given: E_max = 8.0 V, N = 200 turns, A = 0.030 m^2, B = 0.030 T, we find:f = 8.0 / (2π * 200 * 0.030 * 0.030) = 7.1 Hz.

Question 6

If the magnetic field of an electromagnetic wave is in the +x-direction and the electric field of the wave is in the +y-direction,the wave is traveling in the
A) xy-plane.
B) +z-direction.
C) -z-direction.
D) -x-direction.
E) -y-direction.

Accepted Answer

The answer of If the magnetic field of an electromagnetic...

Question 7

A rectangular coil having N turns and measuring 15 cm by 25 cm is rotating in a uniform 1.6-T magnetic field with a frequency of 75 Hz.The rotation axis is perpendicular to the direction of the field.If the coil develops a sinusoidal emf of maximum value 56.9 V,what is the value of N?
A) 2
B) 4
C) 6
D) 8
E) 10

Accepted Answer

The answer of A rectangular coil having N turns and...

Question 8

A closed loop conductor that forms a circle with a radius of 2.0 m is located in a uniform but changing magnetic field.If the maximum emf induced in the loop is 5.0 V,what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies?
A) 0.40 T/s
B) 2.5 T/s
C) 0.080 T/s
D) 5.0 T/s

Accepted Answer

The answer of A closed loop conductor that forms a...

Question 9

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?
A) 100 A/s
B) 1 A/s
C) 1000 A/s
D) 10,000 A/s
E) 10 A/s

Accepted Answer

The induced emf (voltage) in an inductor is given by the formula $V = L \frac{dI}{dt}$, where $V$ is the voltage in volts, $L$ is the inductance in henrys, and $\frac{dI}{dt}$ is the rate of change of current in amperes per second. Rearranging the formula to solve for $\frac{dI}{dt}$, we get $\frac{dI}{dt} = \frac{V}{L}$. Substituting the given values, $V = 1000$ V and $L = 100$ mH = 0.1 H, we find $\frac{dI}{dt} = \frac{1000}{0.1} = 10,000$ A/s.

Question 10

A ten-loop coil having an area of 0.23 m² and a very large resistance is in a 0.047-T uniform magnetic field oriented so that the maximum flux goes through the coil.The coil is then rotated so that the flux through it goes to zero in 0.34 s.What is the magnitude of the average emf induced in the coil during the 0.34 s? A) 0.0032 V B) 0.00 V C) 0.032 V D) 0.32 V E) 1.0 V

Accepted Answer

The answer of A ten-loop coil having an area of...

Question 11

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T • m/A) A) 570 mJ. B) 29 mJ. C) 10 mJ. D) 100 mJ.

Accepted Answer

The energy stored in a magnetic field can be calculated using the formula:
E = (1/2) μ0 V H^2
Where E is the energy stored, μ0 is the magnetic constant, V is the volume of the room, and H is the strength of the magnetic field.

Substituting the given values:
V = 3.0 m x 4.0 m x 2.4 m = 28.8 m^3
H = 5.0 x 10^-5 T
μ0 = 4π x 10^-7 T•m/A

E = (1/2) x 4π x 10^-7 T•m/A x 28.8 m^3 x (5.0 x 10^-5 T)^2
E = 28.8 x 5.0^2 x (4π/2) x 10^-12 J
E = 28.8 x 25 x π x 10^-12 J
E = 2.26 x 10^-9 J

Converting to millijoules:
E = 2.26 x 10^-9 J x 1000 mJ/1 J
E = 2.26 x 10^-6 mJ

Rounding to the nearest whole number, the energy stored in the room due to the earth's magnetic field is 29 mJ, which is answer choice B.

Question 12

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ₀ = 4π × 10^-⁷ T • m/A) A) 865 turns/m B) 472 turns/m C) 1080 turns/m D) 104 turns/m E) 327 turns/m

Accepted Answer

The answer of A solenoid of length 0.700 m having...

Question 13

An electromagnetic wave propagates along the +y direction as shown in the figure.If the electric field at the origin is along the +z direction,what is the direction of the magnetic field? 
A) +z
B) -z
C) +y
D) +x
E) -x

Accepted Answer

The direction of the magnetic field in an electromagnetic wave is perpendicular to both the direction of propagation and the electric field. In this case, since the electric field is along the +z direction and the wave is propagating along the +y direction, the magnetic field must be in the +x direction to satisfy the perpendicularity condition. Therefore, the correct choice is D) +x.

Question 14

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A.If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s,how fast is the current changing?
A) 0.20 A/s
B) 0.40 A/s
C) 0.10 A/s
D) 0.80 A/s

Accepted Answer

The answer of At a certain instant the current flowing...

Question 15

In an electromagnetic wave,the electric and magnetic fields are oriented such that they are
A) parallel to one another and perpendicular to the direction of wave propagation.
B) parallel to one another and parallel to the direction of wave propagation.
C) perpendicular to one another and perpendicular to the direction of wave propagation.
D) perpendicular to one another and parallel to the direction of wave propagation.

Accepted Answer

In an electromagnetic wave, the electric and magnetic fields are always perpendicular to each other and also perpendicular to the direction of wave propagation. This is known as transverse waves. Therefore, option C is the correct choice.

Question 16

Suppose that you wish to construct a simple ac generator having an output of 12 V maximum when rotated at 60 Hz. A uniform magnetic field of 0.050 T is available. If the area of the rotating coil is 100 cm²,how many turns do you need? A) 8 B) 16 C) 32 D) 64 E) 128

Accepted Answer

The answer of Suppose that you wish to construct a...

Question 17

An electromagnetic wave is propagating towards the west.At a certain moment the direction of the magnetic field vector associated with this wave points vertically up.The direction of the electric field vector of this wave is
A) horizontal and pointing south.
B) vertical and pointing down.
C) horizontal and pointing north.
D) vertical and pointing up.
E) horizontal and pointing east.

Accepted Answer

The direction of the electric field vector in an electromagnetic wave is perpendicular to both the magnetic field vector and the direction of propagation. Given the magnetic field points up and the wave propagates west, using the right-hand rule, the electric field points south.

Question 18

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T • m/A) A) 1.2 × 10^-4 J B) 9.6 × 10^-4 J C) 4.8 × 10^-4 J D) 2.4 × 10^-4 J E) 5.9 × 10^-5 J

Accepted Answer

The answer of An insulated wire of diameter 1.0 mm...

Question 19

Wire is wound on a square frame,30 cm by 30 cm,to form a coil of 7 turns.The frame is mounted on a horizontal shaft through its center (perpendicular to the plane of the diagram),as shown in the figure.The coil is in clockwise rotation,with a period of 0.060 s.A uniform,horizontal,magnetic field of magnitude 0.40 T is present.At a given instant,the plane of the coil forms a 60° angle with the horizontal,as shown.At that instant,what is the magnitude of the emf induced in the coil? 
A) 13 V
B) 23 V
C) 2.1 V
D) 3.6 V
E) 26 V

Accepted Answer

The answer of Wire is wound on a square frame,30...

Question 20

A 50-cm wire placed in an east-west direction is moved horizontally to the north with a speed of
2)0 m/s. The horizontal component of the earth's magnetic field at that location is 25 μT toward the north and the vertical component is 50μT downward.What is the emf induced between the ends of the wire?
A) 10 µV
B) 20 µV
C) 30 µV
D) 40 µV
E) 50 µV

Accepted Answer

The answer of A 50-cm wire placed in an east-west...

Quiz 1: A: Foundations

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ0 = 4π × 10-7 T • m/A)

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10-4 m2? (μ0 = 4π × 10-7 T • m/A)

The coil in a 60-Hz ac generator has 125 turns,each having an area of 3.0 × 10-2 m2 and is rotated in a uniform 0.12-T magnetic field.What is the peak output voltage of this generator?

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

If the magnetic field of an electromagnetic wave is in the +x-direction and the electric field of the wave is in the +y-direction,the wave is traveling in the

A rectangular coil having N turns and measuring 15 cm by 25 cm is rotating in a uniform 1.6-T magnetic field with a frequency of 75 Hz.The rotation axis is perpendicular to the direction of the field.If the coil develops a sinusoidal emf of maximum value 56.9 V,what is the value of N?

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10-5 T? (μ0 = 4π × 10-7 T • m/A)

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ0 = 4π × 10-7 T • m/A)

An electromagnetic wave propagates along the +y direction as shown in the figure.If the electric field at the origin is along the +z direction,what is the direction of the magnetic field?

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A.If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s,how fast is the current changing?

In an electromagnetic wave,the electric and magnetic fields are oriented such that they are

Suppose that you wish to construct a simple ac generator having an output of 12 V maximum when rotated at 60 Hz. A uniform magnetic field of 0.050 T is available. If the area of the rotating coil is 100 cm2,how many turns do you need?

An electromagnetic wave is propagating towards the west.At a certain moment the direction of the magnetic field vector associated with this wave points vertically up.The direction of the electric field vector of this wave is

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ0 = 4π × 10-7 T • m/A)

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T • m/A)

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T • m/A)

The coil in a 60-Hz ac generator has 125 turns,each having an area of 3.0 × 10^-2 m² and is rotated in a uniform 0.12-T magnetic field.What is the peak output voltage of this generator?

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

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T • m/A)

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it.What is the winding density of the solenoid? (μ₀ = 4π × 10^-⁷ T • m/A)

Suppose that you wish to construct a simple ac generator having an output of 12 V maximum when rotated at 60 Hz. A uniform magnetic field of 0.050 T is available. If the area of the rotating coil is 100 cm²,how many turns do you need?

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T • m/A)