Question 1

The emf that appears in Faraday's law is:
A) around a conducting circuit
B) around the boundary of the surface used to compute the magnetic flux
C) throughout the surface used to compute the magnetic flux
D) perpendicular to the surface used to compute the magnetic flux
E) none of the above

Accepted Answer

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

Question 2

The magnetic flux Φ_B through a surface: A) is the amount of magnetic field piercing the surface. B) is the magnetic field multiplied by the area. C) does not depend on the area involved. D) is the line integral of the magnetic field around the edge of the surface. E) is the amount of magnetic field skimming along the surface.

Accepted Answer

A

Question 3

1 weber is the same as: A) 1 V.s B) 1 T.s C) 1 T/m D) 1 V/s E) 1 T/m²

Accepted Answer

According to the definition of Weber, it is the amount of magnetic flux that passes through a surface of area 1 square meter perpendicular to a magnetic field of intensity 1 tesla in 1 second. Therefore, one weber can be represented as:
1 Wb = 1 T ⋅ m2/s
From the given options, it is clear that only option A is equivalent to the above expression by changing the units, where V represents volts, F represents farads, s represents seconds, and the subscript numbers indicate the magnitude of the units (e.g. 1F1F1S1 represents 10^-9 farads). Therefore, the correct answer is A.

Question 4

A uniform magnetic field makes an angle of 30 $\degree$with the z axis. If the magnetic flux through a 1.0 m² portion of the xy plane is 5.0 Wb then the magnetic flux through a 2.0 m² portion of the same plane is: A) 2.5 Wb B) 4.3 Wb C) 5.0 Wb D) 5.8 Wb E) 10 Wb

Accepted Answer

The answer of A uniform magnetic field makes an angle...

Question 5

The units of motional emf are: A) volt/second B) volt.meter/second C) volt/tesla D) tesla/second E) tesla.meter²/second

Accepted Answer

The answer of The units of motional emf are:
A) volt/second
B)...

Question 6

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:
A) BAf/2π
B) BAf
C) 2BAf
D) 2 $\pi$BAf
E) 4 $\pi$BAf

Accepted Answer

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

Question 7

The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:
A) magnetic field in X
B) rate of change of magnetic field in X
C) resistance of X
D) thickness of the wire in X
E) current in Y

Accepted Answer

The emf developed in a coil is given by Faraday's law which states that emf = -d(phi_B)/dt, where phi_B is the magnetic flux. Since the magnetic flux in coil X is proportional to the rate of change of magnetic field in coil X (B/dt), the emf developed in coil X due to the current in coil Y is also proportional to the rate of change of magnetic field in coil X. Therefore, the correct choice is B, rate of change of magnetic field in X.

Question 8

The normal to a certain 1.0 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) 0.50 m² B) 0.87 m² C) 1.0 m² D) 1.2 m² E) 2.0 m²

Accepted Answer

The answer of The normal to a certain 1.0 m²...

Question 9

In the experiment shown: 
A) there is a steady reading in G as long as S is closed
B) a motional emf is generated when S is closed
C) the current in the battery goes through G
D) there is a current in G just after S is opened or closed
E) since the two loops are not connected, the current in G is always zero

Accepted Answer

The answer of In the experiment shown: 
A) there is...

Question 10

A rod lies across frictionless rails in a uniform magnetic field B, as shown. The rod moves to the right with speed v. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should: 
A) not change
B) increase linearly with time
C) decrease linearly with time
D) increase quadratically with time
E) decrease quadratically with time

Accepted Answer

The answer of A rod lies across frictionless rails in...

Question 11

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) 0 V B) 1.8 mV C) 3.6 mV D) 6.4 mV E) 23 mV

Accepted Answer

The emf (ε) induced in a conductor moving through a magnetic field is given by ε = 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 direction of motion. Here, B = 0.50 × 10^-4 T, v = 75 km/h = 20.83 m/s (since 75 km/h = 75 * 1000 m / 3600 s), and l = 1.7 m. Thus, ε = 0.50 × 10^-4 T * 20.83 m/s * 1.7 m = 1.78 × 10^-3 V or 1.8 mV.

Question 12

The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the plane of a conducting loop. Rank the four regions indicated on the graph according to the magnitude of the emf induced in the loop, from least to greatest. 
A) 1, 2, 3, 4
B) 2, 4, 3, 1
C) 4, 3, 1, 2
D) 1, 3, 4, 2
E) 4, 3, 2, 1

Accepted Answer

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

Question 13

Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. Now that S is closed, to make the pointer of G deflect toward the right one could: 
A) move the slide of the rheostat R quickly to the right
B) move coil P toward coil Q
C) move coil Q toward coil P
D) open S
E) do none of the above

Accepted Answer

The answer of Coils P and Q each have a...

Question 14

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30 $\degree$ around an edge the flux through it will be:
A) 2.5 Wb
B) 4.3 Wb
C) 5.0 Wb
D) 5.8 Wb
E) 10 Wb

Accepted Answer

The magnetic flux through a surface is given by the formula Φ = B⊥A, where B⊥ is the magnetic field perpendicular to the surface and A is the area of the surface. Since the magnetic field is uniform and perpendicular to the page, the flux through the page is Φ = B⊥A = 5.0 Wb.

When the page is turned by 30° around an edge, the area of the page that is perpendicular to the magnetic field decreases by a factor of cos(30°) = √3/2. Therefore, the new flux through the page is Φ' = B⊥A' = 5.0 Wb x √3/2 ≈ 4.33 Wb.

Therefore, the best choice is B.

Question 15

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected as shown. V₁ reads 1 mV across R. V₂ reads the voltage across the other two resistors, which is: A) 0 V B) 1/3 mV C) 1/2 mV D) 1 mV E) 2 mV

Accepted Answer

The answer of A changing magnetic field pierces the interior...

Question 16

In the circuit shown, there will be a non-zero reading in galvanometer G: 
A) only just after S is closed
B) only just after S is opened
C) only while S is kept closed
D) never
E) only just after S is opened or closed

Accepted Answer

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

Question 17

1 weber is the same as: A) 1 V/s B) 1 T/s C) 1 T/m D) 1 T.m² E) 1 T/m²

Accepted Answer

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

Question 18

Faraday's law states that an induced emf is proportional to:
A) the rate of change of the magnetic field
B) the rate of change of the electric field
C) the rate of change of the magnetic flux
D) the rate of change of the electric flux
E) zero

Accepted Answer

According to Faraday's law, an induced EMF is proportional to the rate of change of magnetic flux.

Question 19

A 2.0 T uniform magnetic field makes an angle of 30 $\degree$ with the z axis. The magnetic flux through a 3.0 m² portion of the xy plane is: A) 2.0 Wb B) 3.0 Wb C) 5.2 Wb D) 6.0 Wb E) 12 Wb

Accepted Answer

We know that the magnetic flux through an area is given by:
Φ=B⋅A⋅cosθ
Where B is the magnetic field, A is the area, and θ is the angle between the magnetic field and the surface normal.
In this case, B=2.0 T and θ=30°. The area is given as 3.0 m×3.0 m = 9.0 m^2.
So, Φ=2.0 T×9.0 m^2×cos30°=15.6 Wb.
However, we are only interested in the magnetic flux through a portion of the xy plane with an area of 3.0 m^2. So, we need to multiply Φ by the ratio of the two areas:
Φ′=(3.0 m^2/9.0 m^2)Φ=5.2 Wb.
Therefore, the best choice is C.

Question 20

If the magnetic flux through a certain region is changing with time:
A) energy must be dissipated as heat
B) an electric field must not exist at the boundary
C) a current must flow around the boundary
D) an emf must exist around the boundary
E) a magnetic field must exist at the boundary

Accepted Answer

This is Faraday's law of electromagnetic induction, which states that a changing magnetic field will induce an electromotive force (emf) around a closed boundary, such as a wire loop. This emf can drive a current in the loop if it is connected to a complete circuit. A and E do not necessarily follow from a changing magnetic field, and B is not true as an electric field is necessary for the induction of an emf. C could be true if a complete circuit exists around the boundary, but it is not a necessary condition.

Quiz 30: Induction and Inductance

The emf that appears in Faraday's law is:

The magnetic flux Φ_B through a surface:

1 weber is the same as:

A uniform magnetic field makes an angle of 30 $\degree$ with the z axis. If the magnetic flux through a 1.0 m² portion of the xy plane is 5.0 Wb then the magnetic flux through a 2.0 m² portion of the same plane is:

The units of motional emf are:

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

The normal to a certain 1.0 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:

In the experiment shown:

A rod lies across frictionless rails in a uniform magnetic field B, as shown. The rod moves to the right with speed v. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should:

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

Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. Now that S is closed, to make the pointer of G deflect toward the right one could:

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30 $\degree$ around an edge the flux through it will be:

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected as shown. V₁ reads 1 mV across R. V₂ reads the voltage across the other two resistors, which is:

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

1 weber is the same as:

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

A 2.0 T uniform magnetic field makes an angle of 30 $\degree$ with the z axis. The magnetic flux through a 3.0 m² portion of the xy plane is:

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

Quiz 30: Induction and Inductance

The emf that appears in Faraday's law is:

The magnetic flux ΦB through a surface:

1 weber is the same as:

A uniform magnetic field makes an angle of 30 °\degree° with the z axis. If the magnetic flux through a 1.0 m2 portion of the xy plane is 5.0 Wb then the magnetic flux through a 2.0 m2 portion of the same plane is:

The units of motional emf are:

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

The normal to a certain 1.0 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:

In the experiment shown:

A rod lies across frictionless rails in a uniform magnetic field B, as shown. The rod moves to the right with speed v. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should:

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

Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. Now that S is closed, to make the pointer of G deflect toward the right one could:

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30 °\degree° around an edge the flux through it will be:

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected as shown. V1 reads 1 mV across R. V2 reads the voltage across the other two resistors, which is:

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

1 weber is the same as:

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

A 2.0 T uniform magnetic field makes an angle of 30 °\degree° with the z axis. The magnetic flux through a 3.0 m2 portion of the xy plane is:

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

The magnetic flux Φ_B through a surface:

A uniform magnetic field makes an angle of 30 $\degree$ with the z axis. If the magnetic flux through a 1.0 m² portion of the xy plane is 5.0 Wb then the magnetic flux through a 2.0 m² portion of the same plane is:

The normal to a certain 1.0 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:

Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30 $\degree$ around an edge the flux through it will be:

A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected as shown. V₁ reads 1 mV across R. V₂ reads the voltage across the other two resistors, which is:

A 2.0 T uniform magnetic field makes an angle of 30 $\degree$ with the z axis. The magnetic flux through a 3.0 m² portion of the xy plane is: