Question 1

A magnet moves inside a coil. Consider the following factors:  Which can affect the emf induced in the coil?

Accepted Answer

I. Velocity of the magnet: The faster the magnet moves, the greater the emf induced in the coil. 
II. Strength of the magnetic field: The stronger the magnetic field, the greater the emf induced in the coil. 
III. Length of the coil: A longer coil can have a higher emf induced, but this is not always the case and depends on other factors such as the number of turns in the coil. Overall, all three factors can affect the emf induced in the coil, so the best choice is E.

Question 2

A 2-T uniform magnetic field makes an angle of 30 $\degree$ with the z axis. The magnetic flux through a 3-m² portion of the xy plane is:

Accepted Answer

The magnetic flux through a surface is given by the equation:
Φ = B · A · cos(θ)
where B is the magnetic field, A is the area of the surface, θ is the angle between the magnetic field and the normal to the surface.
In this problem, B = 2 T (uniform magnetic field), A = 3 m² (portion of the xy plane), and θ = 30°.
So, the magnetic flux through this portion of the xy plane is:
Φ = 2 T · 3 m² · cos(30°) = 5.2 Wb
Therefore, the best choice is C: 5.2 Wb.

Question 3

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected to the same points, as shown. V₁ reads 1 mV. V₂ reads:

Accepted Answer

E

Question 4

In the circuit shown, there will be a non-zero reading in galvanometer G:

Accepted Answer

The answer of In the circuit shown, there will be...

Question 5

If the magnetic flux through a certain region is changing with time:

Accepted Answer

According to Faraday's Law, a changing magnetic flux through a closed loop induces an electromotive force (emf) around the loop, which can lead to a current if there is a complete circuit. Therefore, an emf must exist around the boundary when the magnetic flux through a certain region is changing with time. There may or may not be an electric field or magnetic field at the boundary, and energy dissipation as heat or current flow around the boundary depend on the specific circumstances of the situation.

Question 6

1 weber is the same as:

Accepted Answer

The answer of 1 weber is the same as:
...

Question 7

The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the plane of a conducting loop. Rank the five regions indicated on the graph according to the magnitude of the emf induced in the loop, from least to greatest.

Accepted Answer

The answer of The graph shows the magnitude B of...

Question 8

The normal to a certain 1-m² area makes an angle of 60 $\degree$ with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:

Accepted Answer

Since the normal to the first area makes an angle of 60∘ with the magnetic field, the flux through the first area is given by:
Φ1 = A1 * B * cos(60∘)
where A1 is the area, B is the magnetic field, and cos(60∘) = 0.5

For the flux through the second area to be the same, we need to have:
Φ2 = A2 * B

Equating the two fluxes and substituting for cos(60∘), we get:
A1 * B * 0.5 = A2 * B
Simplifying, we find that:
A2 = 0.5 * A1

Therefore, the second area must be half as large as the first area.
Among the answer choices, only option C has an area that is half of 1 m², so the answer is C.

Question 9

A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is:

Accepted Answer

The answer of A rectangular loop of wire has area...

Question 10

The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit is 0.20 A. At what rate is the magnitude of the magnetic field changing: Is it increasing or decreasing?:

Accepted Answer

The answer of The circuit shown is in a uniform...

Question 11

One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.100 m². The circuit is completed by connecting the coil to a 10- $\pi$ resistor. As the magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other direction, the total charge that flows through the resistor is:

Accepted Answer

The induced emf in the coil is given by:
emf = -N(dΦ/dt),
where N is the number of turns in the coil and Φ is the magnetic flux through the coil.

The magnetic flux through the coil is proportional to the magnetic field intensity and the cross-sectional area of the core:
Φ = B*A = (1.00 T)(0.100 m^2) = 0.100 Wb.

Since the magnetic field changes from 1.00 T in one direction to 1.00 T in the other direction, the change in magnetic field intensity is ΔB = 2.00 T. The time for this change to occur is not given, but we can assume that it happens instantaneously.

Then, the induced emf is:
emf = -N(dΦ/dt) = -N(ΔB/Δt) = -100(2.00 T/Δt) = -200/Δt V.

The current that flows through the circuit is given by Ohm's law:
I = V/R = (200/Δt)/(10 Ω) = 20/Δt A.

The total charge that flows through the circuit is given by:
Q = ∫I dt = I*Δt = (20/Δt)(Δt) = 20 C.

Therefore, the best choice is D) 2 C.

Question 12

Faraday's law states that an induced emf is proportional to:

Accepted Answer

Faraday's law states that the induced electromotive force (emf) in a closed loop is directly proportional to the rate of change of the magnetic flux through the loop. This is expressed mathematically as emf = -dΦ/dt, where Φ is the magnetic flux through the loop and t is time. Therefore, choice C, "the rate of change of the magnetic flux," is the best answer.

Question 13

The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:

Accepted Answer

According to Faraday's law of electromagnetic induction, the emf induced in a coil is proportional to the rate of change of magnetic flux passing through the coil. Since the magnetic field in coil X is produced by the current in neighboring coil Y, the rate of change of the magnetic field in X is directly proportional to the current in Y. Therefore, the emf developed in coil X due to the current in coil Y is proportional to the current in Y, which is option B.

Question 14

In the experiment shown:

Accepted Answer

The answer of In the experiment shown: 
...

Question 15

A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 *10^-⁴ T. The emf induced between the left and right side, separated by 1.7 m, is:

Accepted Answer

The emf induced in a conductor moving in a magnetic field is given by the formula:

emf = Bvl

where B is the magnetic field strength, v is the velocity of the conductor, and l is the length of the conductor perpendicular to the magnetic field.

In this case, the velocity of the car is v = 75 km/h = 20.83 m/s. The length of the conductor is l = 1.7 m. The magnetic field strength is given as B = 0.50 × 10-4 T.

Plugging in these values, we get:

emf = (0.50 × 10-4 T) × (20.83 m/s) × (1.7 m)
emf = 1.79 × 10-5 V = 1.8 mV

So the correct answer is B) 1.8 mV.

Question 16

The units of motional emf are:

Accepted Answer

The answer of The units of motional emf are:
...

Question 17

The emf that appears in Faraday's law is:

Accepted Answer

Faraday's law states that the emf induced in a closed loop is equal to the rate of change of magnetic flux through any surface bounded by the loop. Therefore, the emf appears around the boundary of the surface used to compute the magnetic flux, which is option B.

Question 18

A uniform magnetic field makes an angle of 30 $\degree$ with the z axis. If the magnetic flux through a 1-m² portion of the xy plane is 5 Wb then the magnetic flux through a 2-m² portion of the same plane is:

Accepted Answer

The magnetic flux is proportional to the area when the magnetic field and angle remain constant. Doubling the area from 1 m² to 2 m² doubles the flux from 5 Wb to 10 Wb.

Question 19

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5 Wb. If the page is turned by 30 $\degree$around an edge the flux through it will be:

Accepted Answer

When the page is turned by 30 degrees, the magnetic flux through it will be reduced because the magnetic field lines are now passing through it at an angle rather than perpendicular. 
The new flux can be calculated using the formula: 
new flux = old flux x cos(angle of rotation) 
new flux = 5 Wb x cos(30 degrees) 
new flux = 4.33 Wb (rounded to two decimal places)

Therefore, the best choice is B, 4.3 Wb.

Question 20

1 weber is the same as:

Accepted Answer

The answer of 1 weber is the same as:
...

Quiz 30: Induction and Inductance

A magnet moves inside a coil. Consider the following factors: Which can affect the emf induced in the coil?

A 2-T uniform magnetic field makes an angle of 30 $\degree$ with the z axis. The magnetic flux through a 3-m² portion of the xy plane is:

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected to the same points, as shown. V₁ reads 1 mV. V₂ reads:

In the circuit shown, there will be a non-zero reading in galvanometer G:

If the magnetic flux through a certain region is changing with time:

1 weber is the same as:

The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the plane of a conducting loop. Rank the five regions indicated on the graph according to the magnitude of the emf induced in the loop, from least to greatest.

The normal to a certain 1-m² area makes an angle of 60 $\degree$ with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:

A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is:

The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit is 0.20 A. At what rate is the magnitude of the magnetic field changing: Is it increasing or decreasing?:

Faraday's law states that an induced emf is proportional to:

The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:

In the experiment shown:

A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 *10^-⁴ T. The emf induced between the left and right side, separated by 1.7 m, is:

The units of motional emf are:

The emf that appears in Faraday's law is:

A uniform magnetic field makes an angle of 30 $\degree$ with the z axis. If the magnetic flux through a 1-m² portion of the xy plane is 5 Wb then the magnetic flux through a 2-m² portion of the same plane is:

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5 Wb. If the page is turned by 30 $\degree$ around an edge the flux through it will be:

1 weber is the same as:

Quiz 30: Induction and Inductance

A magnet moves inside a coil. Consider the following factors: Which can affect the emf induced in the coil?

A 2-T uniform magnetic field makes an angle of 30 °\degree° with the z axis. The magnetic flux through a 3-m2 portion of the xy plane is:

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected to the same points, as shown. V1 reads 1 mV. V2 reads:

In the circuit shown, there will be a non-zero reading in galvanometer G:

If the magnetic flux through a certain region is changing with time:

1 weber is the same as:

The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the plane of a conducting loop. Rank the five regions indicated on the graph according to the magnitude of the emf induced in the loop, from least to greatest.

The normal to a certain 1-m2 area makes an angle of 60 °\degree° with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:

A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is:

The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit is 0.20 A. At what rate is the magnitude of the magnetic field changing: Is it increasing or decreasing?:

Faraday's law states that an induced emf is proportional to:

The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:

In the experiment shown:

A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 *10-4 T. The emf induced between the left and right side, separated by 1.7 m, is:

The units of motional emf are:

The emf that appears in Faraday's law is:

A uniform magnetic field makes an angle of 30 °\degree° with the z axis. If the magnetic flux through a 1-m2 portion of the xy plane is 5 Wb then the magnetic flux through a 2-m2 portion of the same plane is:

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5 Wb. If the page is turned by 30 °\degree° around an edge the flux through it will be:

1 weber is the same as:

A 2-T uniform magnetic field makes an angle of 30 $\degree$ with the z axis. The magnetic flux through a 3-m² portion of the xy plane is:

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected to the same points, as shown. V₁ reads 1 mV. V₂ reads:

The normal to a certain 1-m² area makes an angle of 60 $\degree$ with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:

A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 *10^-⁴ T. The emf induced between the left and right side, separated by 1.7 m, is:

A uniform magnetic field makes an angle of 30 $\degree$ with the z axis. If the magnetic flux through a 1-m² portion of the xy plane is 5 Wb then the magnetic flux through a 2-m² portion of the same plane is:

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5 Wb. If the page is turned by 30 $\degree$ around an edge the flux through it will be: