Question 1

The figure shows a uniform,3.0-T magnetic field that is normal to the plane of a conducting,circular loop with a resistance of 1.5 and a radius of 0.024 m.The magnetic field is directed out of the paper as shown.Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. -If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s,what is the magnitude of the average induced emf in the loop? A)8.6 × 10^-³ V B)9.8 × 10^-² V C)2.7 × 10^-² V D)5.4 × 10^-² V E)6.4 × 10^-² V

Accepted Answer

The induced emf in a loop moving through a magnetic field is given by:

emf = -N(dΦ/dt)

where N is the number of turns in the loop and Φ is the magnetic flux through the loop.

In this case, there is only one turn in the loop, so N = 1. The magnetic flux through the loop is given by:

Φ = BA

where B is the magnetic field and A is the area of the loop.

The loop is circular, so A = πr^2, where r is the radius of the loop.

During the 0.2 seconds that the loop is pulled out of the magnetic field, the area of the loop that is inside the field decreases from πr^2 to zero. The average rate of change of the area is:

(dA/dt)ave = (0 - πr^2)/(0.2 s) = -5πr^2 m^2/s

So, the average rate of change of the magnetic flux is:

(dΦ/dt)ave = B(dA/dt)ave = -15πBr^2 V

Therefore, the average induced emf in the loop is:

emf = -N(dΦ/dt)ave = 2.7 × 10^-2 V

Note that the negative sign indicates that the induced current in the loop will be in the opposite direction to the motion of the loop.

Question 2

Which of the following units are equivalent to those of motional emf?
A)T × m/s
B)V × m²/s
C)J/s
D)A × 
E)T × m

Accepted Answer

D

Question 3

The figure shows a uniform magnetic field that is normal to the plane of a conducting loop with resistance R.Which one of the following changes will cause an induced current to flow through the resistor? 
A)decreasing the area of the loop
B)decreasing the magnitude of the magnetic field
C)increasing the magnitude of the magnetic field
D)rotating the loop through 90° about an axis in the plane of the paper
E)all of the above

Accepted Answer

E

Question 4

A long,straight wire is in the same plane as a rectangular,conducting loop.The wire carries a constant current I as shown in the figure.Which one of the following statements is true if the wire is suddenly moved toward the loop? 
A)There will be no induced emf and no induced current.
B)There will be an induced emf,but no induced current.
C)There will be an induced current that is clockwise around the loop.
D)There will be an induced current that is counterclockwise around the loop.
E)There will be an induced electric field that is clockwise around the loop.

Accepted Answer

According to Faraday's law, when a magnetic field flux through a closed loop changes, an induced emf is created in the loop. This induced emf causes a current to flow in such a way as to oppose the change in flux. In this case, when the wire is moved towards the loop, the magnetic field passing through the loop increases. Therefore, an induced emf will be created in the loop, which will cause a current to flow in such a way as to oppose the increase in magnetic field. This can be achieved if the current flows in the opposite direction to the current in the long straight wire. Thus, the induced current will be counterclockwise around the loop, which is option D.

Question 5

A 0.45-m metal rod moves 0.11 m in a direction that is perpendicular to a 0.80-T magnetic field in an elapsed time of 0.036 s.Assuming that the acceleration of the rod is zero m/s²,determine the emf that exists between the ends of the rod. A)1.1 V B)0.27 V C)0.076 V D)9.1 × 10^-⁵ V E)This cannot be determined without knowing the orientation of the rod relative to the magnetic field.

Accepted Answer

The answer of A 0.45-m metal rod moves 0.11 m...

Question 6

A conducting loop has an area of 0.065 m² and is positioned such that a uniform magnetic field is perpendicular to the plane of the loop.When the magnitude of the magnetic field decreases to 0.30 T in 0.087 s,the average induced emf in the loop is 1.2 V.What is the initial value of the magnetic field?
A)0.42 T
B)0.75 T
C)0.87 T
D)1.2 T
E)1.9 T

Accepted Answer

The answer of A conducting loop has an area of...

Question 7

The figure shows a uniform,3.0-T magnetic field that is normal to the plane of a conducting,circular loop with a resistance of 1.5 and a radius of 0.024 m.The magnetic field is directed out of the paper as shown.Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. -If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s,at what rate is energy dissipated in R? A)1.8 × 10^-² W B)3.6 × 10^-² W C)3.8 × 10^-³ W D)2.7 × 10^-⁴ W E)4.9 × 10^-⁴ W

Accepted Answer

The answer of The figure shows a uniform,3.0-T magnetic field...

Question 8

The figure shows a uniform,3.0-T magnetic field that is normal to the plane of a conducting,circular loop with a resistance of 1.5 and a radius of 0.024 m.The magnetic field is directed out of the paper as shown.Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. -What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s? A)2.8 × 10^-³ A,clockwise B)4.5 × 10^-³ A,clockwise C)4.5 × 10^-³ A,counterclockwise D)9.0 × 10^-³ A,clockwise E)9.0 × 10^-³ A,counterclockwise

Accepted Answer

The magnetic flux through the circular loop is given by:
Φ = BA, where B is the magnetic field, and A is the area of the loop.
Since the magnetic field is normal to the plane of the loop, the angle between B and A is 0 degrees, so the flux simplifies to:
Φ = BA = Bπr²
where r is the radius of the loop.
The induced emf in the loop is given by:
ε = -dΦ/dt
Since the magnetic field is doubled in 0.4 seconds, the rate of change of flux is:
dΦ/dt = Bπr²/Δt = (2B)πr²/0.4
ε = -(2Bπr²/0.4) = -5Bπr²
The current in the loop is given by:
I = ε/R
where R is the resistance of the loop.
I = (-5Bπr²)/R = (-5(3.0 T)(π)(0.024 m)²)/(1.5 Ω) = -9.0 × 10³ A
The negative sign indicates that the current is flowing in the clockwise direction. Taking the absolute value, we get:
|I| = 9.0 × 10³ A
Therefore, the answer is D.

Question 9

A uniform magnetic field passes through two areas,A₁ and A₂.The angles between the magnetic field and the normals of areas A₁ and A₂ are 30.0° and 60.0°,respectively.If the magnetic flux through the two areas is the same,what is the ratio A₁/A₂?
A)0.354
B)0.866
C)1.00
D)1.23
E)1.73

Accepted Answer

The magnetic flux through an area is given by the equation Φ = BAcosθ, where B is the magnetic field strength, A is the area, and θ is the angle between the magnetic field and the normal to the area. If the magnetic flux through two areas is the same, then BAcosθ1 = BAcosθ2. Since the magnetic field strength is the same for both areas, we can divide both sides of the equation by B to get Acosθ1 = Acosθ2. Substituting the given angles, we get Acos30° = Acos60°. Solving for the ratio A1/A2, we get A1/A2 = cos60°/cos30° = 0.866.

Question 10

A 250-turn solenoid carries a current of 9.0 A.The radius of the solenoid is 0.075 m;and its length is 0.14 m.Determine the magnetic flux through the circular cross-sectional area at the center of the solenoid. A)1.8 × 10^-⁵ Wb B)9.9 × 10^-⁵ Wb C)3.6 × 10^-⁴ Wb D)7.0 × 10^-⁴ Wb E)2.2 × 10^-³ Wb

Accepted Answer

The magnetic flux through the circular cross-sectional area at the center of the solenoid can be calculated using the formula:

ϕ = μ₀n²πr²I

where μ₀ is the permeability of free space (4π x 10^-7 T m/A), n is the number of turns per unit length (n = N/L), N is the total number of turns (N = 250), L is the length of the solenoid (L = 0.14 m), r is the radius of the solenoid (r = 0.075 m), and I is the current (I = 9.0 A).

Substituting the values:

n = N/L = 250/0.14 = 1785.71 turns/m
ϕ = (4π x 10^-7 T m/A) x (1785.71 turns/m)² x π x (0.075 m)² x 9.0 A
ϕ = 3.6 x 10^-4 Wb
ϕ = 3.6 x 10^4 μWb

Therefore, the magnetic flux through the circular cross-sectional area at the center of the solenoid is 3.6 x 10^-4 Wb or 3.6 x 10^4 μWb, which is closest to the option C (3.6 × 10⁴ μWb).

Question 11

The figure shows a uniform,3.0-T magnetic field that is normal to the plane of a conducting,circular loop with a resistance of 1.5 and a radius of 0.024 m.The magnetic field is directed out of the paper as shown.Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop.
 
-What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in 0.4 s?
A)0.43 V
B)0.65 V
C)0.014 V
D)0.027 V
E)0.038 V

Accepted Answer

The answer of The figure shows a uniform,3.0-T magnetic field...

Question 12

A 0.60-T magnetic field is directed perpendicular to the plane of a circular loop of radius 0.40 m.What is the magnitude of the magnetic flux through the loop?
A)0.049 Wb
B)0.098 Wb
C)0.24 Wb
D)0.30 Wb
E)zero Wb

Accepted Answer

The answer of A 0.60-T magnetic field is directed perpendicular...

Question 13

A 1.2-kg rod that has a length of 1.0 m and a resistance of 5.0  slides with constant speed down a pair of frictionless vertical conducting rails that are joined at the bottom.Other than the rod,the rest of the circuit is resistanceless.A uniform magnetic field of magnitude 3.0 T is perpendicular to the plane formed by the rod and the rails as shown.Determine the speed of the rod. 
A)0.38 m/s
B)0.90 m/s
C)2.6 m/s
D)6.5 m/s
E)8.7 m/s

Accepted Answer

The answer of A 1.2-kg rod that has a length...

Question 14

The Earth's magnetic field passes through a square tabletop with a magnitude of 4.95 × 10^-⁵ T and is directed at an angle of 165° relative to the normal of the tabletop.If the tabletop has 1.50-m sides,what is the magnitude of the magnetic flux through it? A)1.08 × 10^-⁴ Wb B)7.11 × 10^-⁵ Wb C)2.88 × 10^-⁵ Wb D)1.92 × 10^-⁵ Wb E)3.30 × 10^-⁶ Wb

Accepted Answer

The magnetic flux through the tabletop is given by the product of the magnetic field strength, the area of the tabletop, and the cosine of the angle between the magnetic field and the normal to the tabletop. In this case, the magnetic field strength is 4.95 × 10^-5 T, the area of the tabletop is 1.50 m^2, and the angle between the magnetic field and the normal to the tabletop is 165°. Therefore, the magnetic flux through the tabletop is:$$\Phi_B = B A \cos	heta = (4.95 	imes 10^{-5} 	ext{ T})(1.50 	ext{ m}^2)(\cos 165°) = 1.08 	imes 10^{-4} 	ext{ Wb}$$

Question 15

A conducting loop of wire is placed in a magnetic field that is normal to the plane of the loop.Which one of the following actions will not result in an induced current in the loop?
A)Rotate the loop about an axis that is parallel to the field and passes through the center of the loop.
B)Increase the strength of the magnetic field.
C)Decrease the area of the loop.
D)Decrease the strength of the magnetic field.
E)Rotate the loop about an axis that is perpendicular to the field and passes through the center of the loop.

Accepted Answer

Rotating the loop about an axis parallel to the magnetic field does not change the magnetic flux through the loop, hence no induced current is generated according to Faraday's law of electromagnetic induction.

Question 16

A circular coil of wire has 25 turns and has a radius of 0.075 m.The coil is located in a variable magnetic field whose behavior is shown on the graph.At all times,the magnetic field is directed at an angle of 75° relative to the normal to the plane of a loop.What is the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s? 
A)-18 mV
B)-49 mV
C)-92 mV
D)-140 mV
E)-180 mV

Accepted Answer

The answer of A circular coil of wire has 25...

Question 17

A circular copper loop is placed perpendicular to a uniform magnetic field of 0.75 T.Due to external forces,the area of the loop decreases at a rate of 7.26 × 10^-³ m²/s.Determine the induced emf in the loop. A)3.1 × 10^-⁴ V B)6.3 × 10^-⁴ V C)1.2 × 10^-³ V D)5.4 × 10^-³ V E)3.1 V

Accepted Answer

The answer of A circular copper loop is placed perpendicular...

Question 18

A long,straight wire is in the same plane as a wooden,non-conducting loop.The wire carries an increasing current I in the direction shown in the figure. 
A)There will be no induced emf and no induced current.
B)There will be a counterclockwise induced emf,but no induced current.
C)There will be a clockwise induced emf,but no induced current.
D)There will be a clockwise induced current in the loop.
E)There will be a counterclockwise induced current in the loop.

Accepted Answer

The answer of A long,straight wire is in the same...

Question 19

A magnetic field is directed perpendicular to the plane of a 0.15-m × 0.30-m rectangular coil consisting of 240 loops of wire.To induce an average emf of -2.5 V in the coil,the magnetic field is increased from 0.1 T to 1.8 T during a time interval .Determine .
A)0.053 s
B)0.13 s
C)12 s
D)6.4 s
E)7.3 s

Accepted Answer

The answer of A magnetic field is directed perpendicular to...

Question 20

A conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown.As a result of the bar moving through a constant magnetic field,a current I is induced in the indicated direction.Which one of the following directions is that of the magnetic field? 
A)toward the right
B)toward the left
C)parallel to the long axis of the bar
D)into the page
E)out of the page

Accepted Answer

The answer of A conducting bar moves to the left...

Quiz 22: Electromagnetic Induction

Which of the following units are equivalent to those of motional emf?

The figure shows a uniform magnetic field that is normal to the plane of a conducting loop with resistance R.Which one of the following changes will cause an induced current to flow through the resistor?

A long,straight wire is in the same plane as a rectangular,conducting loop.The wire carries a constant current I as shown in the figure.Which one of the following statements is true if the wire is suddenly moved toward the loop?

A 0.45-m metal rod moves 0.11 m in a direction that is perpendicular to a 0.80-T magnetic field in an elapsed time of 0.036 s.Assuming that the acceleration of the rod is zero m/s²,determine the emf that exists between the ends of the rod.

A uniform magnetic field passes through two areas,A₁ and A₂.The angles between the magnetic field and the normals of areas A₁ and A₂ are 30.0° and 60.0°,respectively.If the magnetic flux through the two areas is the same,what is the ratio A₁/A₂?

A 250-turn solenoid carries a current of 9.0 A.The radius of the solenoid is 0.075 m;and its length is 0.14 m.Determine the magnetic flux through the circular cross-sectional area at the center of the solenoid.

A 0.60-T magnetic field is directed perpendicular to the plane of a circular loop of radius 0.40 m.What is the magnitude of the magnetic flux through the loop?

The Earth's magnetic field passes through a square tabletop with a magnitude of 4.95 × 10-⁵ T and is directed at an angle of 165° relative to the normal of the tabletop.If the tabletop has 1.50-m sides,what is the magnitude of the magnetic flux through it?

A conducting loop of wire is placed in a magnetic field that is normal to the plane of the loop.Which one of the following actions will not result in an induced current in the loop?

A circular copper loop is placed perpendicular to a uniform magnetic field of 0.75 T.Due to external forces,the area of the loop decreases at a rate of 7.26 × 10-³ m²/s.Determine the induced emf in the loop.

A long,straight wire is in the same plane as a wooden,non-conducting loop.The wire carries an increasing current I in the direction shown in the figure.

A conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown.As a result of the bar moving through a constant magnetic field,a current I is induced in the indicated direction.Which one of the following directions is that of the magnetic field?

The Earth's magnetic field passes through a square tabletop with a magnitude of 4.95 × 10^-⁵ T and is directed at an angle of 165° relative to the normal of the tabletop.If the tabletop has 1.50-m sides,what is the magnitude of the magnetic flux through it?

A circular copper loop is placed perpendicular to a uniform magnetic field of 0.75 T.Due to external forces,the area of the loop decreases at a rate of 7.26 × 10^-³ m²/s.Determine the induced emf in the loop.