Question 1

A straight wire lies along the y-axis initially carrying a current of 10 A in the positive y-direction.The current decreases and reverses to 10 A in the negative y-direction,the change in current happening at a uniform rate.In the 1st quadrant a square conducting coil has 2 sides parallel to the y-axis and the other 2 sides parallel to the x-axis.The side of the coil nearest and parallel to the straight wire is at a distance equal to the length of one of the sides of the square.As the current is going from 10 A in one direction to 10 A in the other,in which direction is the induced current in this side of the square coil nearest to the straight wire?

Accepted Answer

The magnetic field due to the straight wire is in the positive x-direction. As the current decreases, the magnetic field decreases, inducing an emf in the coil. The direction of the induced current is such that it creates a magnetic field that opposes the change in the original magnetic field. Therefore, the induced current in the side of the coil nearest to the straight wire is in the positive y-direction.

Question 2

A 41-turn square coil of area 0.074 m² and a 123-turn circular coil are both placed perpendicular 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?

Accepted Answer

The induced voltage in a coil is given by the equation V = NAB/Δt, where N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, and Δt is the time interval over which the magnetic field changes. Since the voltage induced in both coils is the same, we have:
N1A1 = N2A2
where N1 = 41, A1 = 0.074 m2, N2 = 123, and we need to find A2. Therefore:
A2 = (N1/N2)A1 = (41/123) × 0.074 m2 ≈ 0.025 m2
Therefore, the answer is (C) 0.025 m2.

Question 3

A wire loop of radius 0.250 m is placed in a uniform magnetic field of magnitude 0.740 T. The field is directed perpendicular to the plane of the loop. -If the area of the loop increases at a rate of area 1.50 * 10^-3 m²/s,what is the magnitude of the emf induced in the coil?

Accepted Answer

The magnitude of the emf induced in the coil can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf (ε) in a circuit is equal to the rate of change of the magnetic flux through the circuit. The formula for emf is ε = -dΦ/dt, where Φ is the magnetic flux. The magnetic flux (Φ) through the loop is given by Φ = B*A, where B is the magnetic field strength and A is the area of the loop. Given that the area of the loop increases at a rate of 1.50 x 10^-3 m^2/s, and the magnetic field strength is 0.740 T, the rate of change of magnetic flux dΦ/dt = B * dA/dt = 0.740 T * 1.50 x 10^-3 m^2/s = 1.11 x 10^-3 T*m^2/s = 1.11 mV. Therefore, the magnitude of the induced emf is 1.11 mV.

Question 4

The magnet moving past an object will produce eddy currents in the object if the object:

Accepted Answer

Eddy currents are induced electrical currents that are generated in conductive materials as a result of a changing magnetic field. Therefore, the object must be a conductor in order for eddy currents to be produced. Magnetic materials alone will not produce eddy currents, while insulators and liquids may not be conductive enough to allow for significant eddy current production.

Question 5

A plane with a wingspan of 35.0 m is flying horizontally at a speed of 280 m/s over a location where the Earth's magnetic field is 45.0 μT at 55° below the horizontal.What voltage is generated between the wingtips?

Accepted Answer

The voltage (emf) generated is given by the formula: emf = B * v * L * sin(θ), where B is the magnetic field strength, v is the velocity, L is the wingspan, and θ is the angle of the magnetic field with respect to the horizontal. Substituting the given values: emf = 45.0E-6 T * 280 m/s * 35.0 m * sin(55°) ≈ 0.36 V.

Question 6

An airplane with a wingspan of 79.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.490 × l0−⁴ T.If the induced potential between wingtips is 0.875 V,what is the plane's speed?

Accepted Answer

The induced potential (voltage) $V$ in a conductor moving through a magnetic field is given by the equation $V = Blv$, where $B$ is the magnetic field strength, $l$ is the length of the conductor (in this case, the wingspan of the airplane), and $v$ is the velocity of the conductor (the speed of the airplane). Rearranging this formula to solve for $v$, we get $v = \frac{V}{Bl}$.Given:- $B = 0.490 \times 10^{-4} \, \text{T}$ (the downward component of the Earth's magnetic field)- $l = 79.0 \, \text{m}$ (the wingspan of the airplane)- $V = 0.875 \, \text{V}$ (the induced potential between wingtips)Substituting these values into the formula gives:$$v = \frac{0.875}{(0.490 \times 10^{-4}) \times 79.0} \approx 226 \, \text{m/s}$$Therefore, the plane's speed is approximately 226 m/s.

Question 7

A planar loop consisting of seven turns of wire,each of which encloses 200 cm²,is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 14 × 10^-3 T to 38 × 10^-3T in a time of 8.0 × 10^-3s.What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω?

Accepted Answer

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

Question 8

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.The induced current will be greatest in magnitude when the magnet is located so that

Accepted Answer

The induced current is greatest when the rate of change of magnetic flux through the loop is greatest, which occurs when the loop is near either the north or the south pole of the magnet.

Question 9

A wire loop of radius 0.250 m is placed in a uniform magnetic field of magnitude 0.740 T. The field is directed perpendicular to the plane of the loop. 
-If the field reverses its direction,and its magnitude changes to 0.100 T in time 1.06 s,what is the magnitude of the average induced emf in the loop during this time?

Accepted Answer

The magnitude of the average induced emf can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf ($\epsilon$) in a loop is equal to the rate of change of magnetic flux ($\Phi_B$) through the loop. Mathematically, this is given by $\epsilon = -\Delta \Phi_B / \Delta t$, where $\Delta \Phi_B$ is the change in magnetic flux and $\Delta t$ is the time over which this change occurs.The magnetic flux $\Phi_B$ through the loop is given by $\Phi_B = B \cdot A \cdot \cos(\theta)$, where $B$ is the magnetic field strength, $A$ is the area of the loop, and $\theta$ is the angle between the magnetic field and the normal to the plane of the loop. Since the field is perpendicular to the loop, $\cos(\theta) = 1$, simplifying the expression to $\Phi_B = B \cdot A$.Given that the radius of the loop is 0.250 m, the area $A$ of the loop is $\pi r^2 = \pi \cdot (0.250)^2$ m$^2$. The change in magnetic field $\Delta B$ is from 0.740 T to -0.100 T (a total change of 0.840 T, since it reverses direction and decreases in magnitude), and the change in time $\Delta t$ is 1.06 s.The change in magnetic flux $\Delta \Phi_B$ is then $\Delta B \cdot A = 0.840 \cdot \pi \cdot (0.250)^2$. Plugging this into the formula for induced emf gives:$$\epsilon = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{0.840 \cdot \pi \cdot (0.250)^2}{1.06}$$Calculating this gives:$$\epsilon = -\frac{0.840 \cdot 3.1416 \cdot 0.0625}{1.06} \approx -0.156 \text{ V} = 156 \text{ mV}$$The negative sign indicates the direction of the induced emf (opposite to the change in flux), but since the question asks for the magnitude, we take the absolute value, which is 156 mV.

Question 10

A metal rod is falling toward the surface of the Earth near the equator.As it falls,one end of the rod becomes positively charged due to the motional emf of the rod through the Earth's magnetic field.The rod is oriented so that

Accepted Answer

The Earth's magnetic field lines are approximately horizontal and points toward the geographic north in the northern hemisphere. As the metal rod falls, it cuts across these magnetic field lines and generates a motional emf. According to the right-hand rule, the direction of the induced current will be perpendicular to both the direction of motion and the magnetic field direction. Therefore, the positive end of the rod will point in the direction perpendicular to the velocity and the magnetic field, which is toward the east.

Question 11

A circular loop is suspended in a uniform magnetic field as shown in the figure. 
​
If the loop area increases,what affect does this have on the induced current?

Accepted Answer

The answer of A circular loop is suspended in a...

Question 12

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.As the south pole leaves the loop of wire,the induced current (as viewed from above)will be

Accepted Answer

As the south pole leaves the loop, the magnetic flux through the loop decreases, inducing a current that opposes this change. According to Lenz's Law, the induced current will be clockwise to create a magnetic field that opposes the decrease in flux.

Question 13

A flat coil of wire consisting of 15 turns,each with an area of 40 cm²,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 1.5 T to 5.1 T in 2.0 s.If the coil has a total resistance of 0.20 Ω,what is the magnitude of the induced current?

Accepted Answer

The magnetic flux through the coil is given by:
Φ = NAB
where N = 15 is the number of turns, A = 40 cm² = 0.004 m² is the area of each turn, and B is the magnetic field strength.
During the 2.0 s time interval, the magnetic field strength changes from 1.5 T to 5.1 T at a constant rate, so the average magnetic field strength is:
B_avg = (1.5 T + 5.1 T)/2 = 3.3 T
Therefore, the average magnetic flux through the coil is:
Φ_avg = NAB_avg = 15 x 0.004 m² x 3.3 T = 0.198 Wb
Using Faraday's law of electromagnetic induction, the magnitude of the induced emf in the coil is given by:
ε = -dΦ/dt
where ε is the induced emf and dt = 2.0 s is the time interval during which the magnetic field strength changes.
The rate of change of magnetic flux is:
dΦ/dt = ΔΦ/Δt = (0.198 Wb - 0 Wb)/2.0 s = 0.099 V
Therefore, the magnitude of the induced emf is:
ε = -dΦ/dt = -0.099 V
The induced emf causes a current to flow in the coil, which is given by Ohm's law:
I = ε/R
where R = 0.20 Ω is the total resistance of the coil.
Substituting the values, we get:
I = (-0.099 V)/(0.20 Ω) = -0.495 A
The negative sign indicates that the induced current flows in the opposite direction to the direction of the rate of change of magnetic flux. Therefore, the magnitude of the induced current is:
|I| = 0.495 A = 5.40E-1 A (to two significant figures)

Question 14

A bar magnet is held stationary while a circular loop of wire is moved toward the magnet at constant velocity at position A as in the figure. 
The loop passes over the magnet's center at position B and moves away from the magnet at position C.Viewing the loop from the left as indicated in the figure,for which position is the induced current zero?

Accepted Answer

According to Faraday's Law of Induction, a changing magnetic field can induce an electric current in a loop of wire. As the loop is moved toward the magnet at position A, the magnetic field in the loop increases, creating an induced current in the opposite direction. At position B, the loop is directly above the magnet's center where the magnetic field is maximum and unchanging, so there is no change in the magnetic field and therefore no induced current. At position C, the loop moves away from the magnet, causing the magnetic field to decrease and inducing a current in the opposite direction to its motion toward the magnet. Therefore, the induced current is zero at position B.

Question 15

A square coil,enclosing an area with sides 2.75 cm long,is wrapped with 1 875 turns of wire.A uniform magnetic field perpendicular to its plane is turned on and increases to 0.390 T during an interval of 1.70 s.What average voltage is induced in the coil?

Accepted Answer

The average voltage induced in the coil is given by the equation:ε = -N * (ΔΦ / Δt)where:ε is the average voltage induced in the coil (in volts)N is the number of turns in the coilΔΦ is the change in magnetic flux through the coil (in webers)Δt is the time interval over which the change in magnetic flux occurs (in seconds)In this problem, we are given the following information:N = 1875 turnsΔΦ = B * A = (0.390 T) * (2.75 cm * 2.75 cm) = 2.71 * 10^-4 WbΔt = 1.70 sSubstituting these values into the equation, we get:ε = -N * (ΔΦ / Δt) = -(1875 turns) * (2.71 * 10^-4 Wb / 1.70 s) = 0.325 VTherefore, the average voltage induced in the coil is 0.325 V, which corresponds to choice A.

Question 16

A straight wire of length 
Is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.Which end of the rod is positively charged?

Accepted Answer

When a straight wire moves in a magnetic field at a constant velocity, a potential difference is produced between its two ends, causing an electric field to develop.

The direction of this electric field can be determined by the Fleming's right-hand rule. In this situation, the thumb of the right hand points in the direction of the velocity (downward), the index finger points in the direction of the magnetic field (north), and the middle finger points in the direction of the electric field.

Using Fleming’s rule, we can see that the electric field will point towards the east end of the wire, meaning that the east end will be more positively charged than the west end. Therefore, the answer is B) the east end.

Question 17

If a bar magnet is falling through a loop of wire,the induced current in the loop of wire sets up a field which exerts a force on the magnet.This force between the magnet and the loop will be attractive when

Accepted Answer

When the magnet is entering the loop, the induced current initially opposes the motion of the magnet, resulting in a repulsive force. When the magnet is halfway through, the induced current is maximum and the force is zero. When the magnet is leaving the loop, the induced current opposes the decrease in the magnetic field, resulting in an attractive force between the magnet and the loop. Therefore, the best choice is C).

Question 18

A straight wire of length l is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.If the resistance of the rod is R,what is the current through the rod?

Accepted Answer

The answer of A straight wire of length l is...

Question 19

A bar magnet is falling through a loop of wire with constant velocity.The south pole enters first.As the magnet leaves the wire,the induced current (as viewed from above):

Accepted Answer

According to Faraday's law, a changing magnetic field (in this case, a decreasing field as the magnet moves away) induces an electric current in a nearby conductor. The direction of this induced current follows Lenz's law, which states that the induced current will flow in a direction that opposes the change that produced it. When the south pole of the magnet enters the loop, a magnetic field is produced that induces a current in the loop. This current will flow counterclockwise as viewed from above, in a direction that opposes the motion of the south pole into the loop. As the magnet leaves the loop, the induced current will continue to oppose the motion of the magnet and will flow clockwise as viewed from above.

Question 20

A bar magnet is held above the center of a conducting ring in the horizontal plane.The magnet is dropped so it falls lengthwise toward the center of the ring.Will the falling magnet be attracted toward the ring or be repelled by the ring due to the magnetic interaction of the magnet and the ring?

Accepted Answer

The falling magnet induces a current in the conducting ring, which in turn creates its own magnetic field according to Lenz's Law. This induced magnetic field opposes the change that caused it, meaning it will generate a magnetic field that repels the falling magnet, regardless of which pole is leading.

Quiz 20: Induced Voltages and Inductance

A 41-turn square coil of area 0.074 m² and a 123-turn circular coil are both placed perpendicular 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 wire loop of radius 0.250 m is placed in a uniform magnetic field of magnitude 0.740 T. The field is directed perpendicular to the plane of the loop. -If the area of the loop increases at a rate of area 1.50 * 10^-3 m²/s,what is the magnitude of the emf induced in the coil?

The magnet moving past an object will produce eddy currents in the object if the object:

A plane with a wingspan of 35.0 m is flying horizontally at a speed of 280 m/s over a location where the Earth's magnetic field is 45.0 μT at 55° below the horizontal.What voltage is generated between the wingtips?

An airplane with a wingspan of 79.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.490 × l0−⁴ T.If the induced potential between wingtips is 0.875 V,what is the plane's speed?

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.The induced current will be greatest in magnitude when the magnet is located so that

A metal rod is falling toward the surface of the Earth near the equator.As it falls,one end of the rod becomes positively charged due to the motional emf of the rod through the Earth's magnetic field.The rod is oriented so that

A circular loop is suspended in a uniform magnetic field as shown in the figure. If the loop area increases,what affect does this have on the induced current?

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.As the south pole leaves the loop of wire,the induced current (as viewed from above) will be

A flat coil of wire consisting of 15 turns,each with an area of 40 cm²,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 1.5 T to 5.1 T in 2.0 s.If the coil has a total resistance of 0.20 Ω,what is the magnitude of the induced current?

A square coil,enclosing an area with sides 2.75 cm long,is wrapped with 1 875 turns of wire.A uniform magnetic field perpendicular to its plane is turned on and increases to 0.390 T during an interval of 1.70 s.What average voltage is induced in the coil?

A straight wire of length Is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.Which end of the rod is positively charged?

If a bar magnet is falling through a loop of wire,the induced current in the loop of wire sets up a field which exerts a force on the magnet.This force between the magnet and the loop will be attractive when

A straight wire of length l is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.If the resistance of the rod is R,what is the current through the rod?

A bar magnet is falling through a loop of wire with constant velocity.The south pole enters first.As the magnet leaves the wire,the induced current (as viewed from above) :

A bar magnet is held above the center of a conducting ring in the horizontal plane.The magnet is dropped so it falls lengthwise toward the center of the ring.Will the falling magnet be attracted toward the ring or be repelled by the ring due to the magnetic interaction of the magnet and the ring?

Quiz 20: Induced Voltages and Inductance

A 41-turn square coil of area 0.074 m2 and a 123-turn circular coil are both placed perpendicular 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 wire loop of radius 0.250 m is placed in a uniform magnetic field of magnitude 0.740 T. The field is directed perpendicular to the plane of the loop. -If the area of the loop increases at a rate of area 1.50 * 10-3 m2/s,what is the magnitude of the emf induced in the coil?

The magnet moving past an object will produce eddy currents in the object if the object:

A plane with a wingspan of 35.0 m is flying horizontally at a speed of 280 m/s over a location where the Earth's magnetic field is 45.0 μT at 55° below the horizontal.What voltage is generated between the wingtips?

An airplane with a wingspan of 79.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.490 × l0−4 T.If the induced potential between wingtips is 0.875 V,what is the plane's speed?

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.The induced current will be greatest in magnitude when the magnet is located so that

A metal rod is falling toward the surface of the Earth near the equator.As it falls,one end of the rod becomes positively charged due to the motional emf of the rod through the Earth's magnetic field.The rod is oriented so that

A circular loop is suspended in a uniform magnetic field as shown in the figure. ​ If the loop area increases,what affect does this have on the induced current?

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.As the south pole leaves the loop of wire,the induced current (as viewed from above) will be

A flat coil of wire consisting of 15 turns,each with an area of 40 cm2,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 1.5 T to 5.1 T in 2.0 s.If the coil has a total resistance of 0.20 Ω,what is the magnitude of the induced current?

A square coil,enclosing an area with sides 2.75 cm long,is wrapped with 1 875 turns of wire.A uniform magnetic field perpendicular to its plane is turned on and increases to 0.390 T during an interval of 1.70 s.What average voltage is induced in the coil?

A straight wire of length Is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.Which end of the rod is positively charged?

If a bar magnet is falling through a loop of wire,the induced current in the loop of wire sets up a field which exerts a force on the magnet.This force between the magnet and the loop will be attractive when

A straight wire of length l is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.If the resistance of the rod is R,what is the current through the rod?

A bar magnet is falling through a loop of wire with constant velocity.The south pole enters first.As the magnet leaves the wire,the induced current (as viewed from above) :

A bar magnet is held above the center of a conducting ring in the horizontal plane.The magnet is dropped so it falls lengthwise toward the center of the ring.Will the falling magnet be attracted toward the ring or be repelled by the ring due to the magnetic interaction of the magnet and the ring?

A 41-turn square coil of area 0.074 m² and a 123-turn circular coil are both placed perpendicular 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 wire loop of radius 0.250 m is placed in a uniform magnetic field of magnitude 0.740 T. The field is directed perpendicular to the plane of the loop. -If the area of the loop increases at a rate of area 1.50 * 10^-3 m²/s,what is the magnitude of the emf induced in the coil?

An airplane with a wingspan of 79.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.490 × l0−⁴ T.If the induced potential between wingtips is 0.875 V,what is the plane's speed?

A circular loop is suspended in a uniform magnetic field as shown in the figure. If the loop area increases,what affect does this have on the induced current?

A flat coil of wire consisting of 15 turns,each with an area of 40 cm²,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 1.5 T to 5.1 T in 2.0 s.If the coil has a total resistance of 0.20 Ω,what is the magnitude of the induced current?