A thin film of oil with index of refraction n = 1.6 and thickness t = 75 nm floats on water. The oil is illuminated from above, perpendicular to the surface.
Part A): What is the longest wavelength of light, in nanometers, that will undergo destructive interference when it is shone on the oil?
Part B): What is the next longest wavelength of light, in nanometers, that will undergo destructive interference when it is shone on the oil?
Part C): What is the longest wavelength of light, in nanometers, that will undergo constructive interference when it is shone on the oil?

The final image is approximately 3.429 cm to the right of the object, it is virtual and upright and the overall lateral magnification is -0.545.

What is lateral magnification?

Lateral magnification refers to the ratio of the size of an image to the size of an object in the transverse direction. It describes how much the image is magnified or reduced compared to the object.

(a) To find the position of the final image using the thin-lens equation, we can use the following formula:

1/f = 1/dᵢ - 1/dₒ

where:

f is the focal length of the lens,

dᵢ is the image distance,

dₒ is the object distance.

For the first lens (converging lens) with a focal length of 8.1 cm, the object distance (dₒ) is 16.2 cm.

1/8.1 = 1/dᵢ - 1/16.2

Simplifying the equation, we get:

dᵢ = 1 / (1/8.1 + 1/16.2)

dᵢ ≈ 5.405 cm

So, the position of the image formed by the first lens is approximately 5.405 cm to the right of the object.

Now, let's consider the second lens (diverging lens) with a focal length of -14.6 cm. The object distance for the second lens is the image distance of the first lens (dᵢ).

Using the same thin-lens equation, we have:

1/(-14.6) = 1/d - 1/5.405

Solving for d, we get:

d ≈ -8.834 cm

Since the value is negative, it indicates that the image formed by the second lens is virtual and located 8.834 cm to the left of the second lens.

To find the position of the final image, we sum the distances:

Position of the final image = dᵢ + d ≈ 5.405 cm + (-8.834 cm) ≈ -3.429 cm

Therefore, the final image is approximately 3.429 cm to the right of the object.

(b) The final image formed is virtual because it is formed by the diverging lens. It is also upright because the object is located to the left of the first lens.

(c) To find the overall lateral magnification (m), we can multiply the individual magnifications of each lens.

The magnification of a lens is given by the formula:

m = -dᵢ / dₒ

For the first lens, the magnification (m₁) is:

m₁ = -dᵢ / dₒ = -5.405 cm / 16.2 cm ≈ -0.333

For the second lens, the magnification (m₂) is:

m₂ = -d / dᵢ = -(-8.834 cm) / 5.405 cm ≈ 1.635

The overall magnification (m) is the product of the individual magnifications:

m = m₁ * m₂ ≈ (-0.333) * (1.635) ≈ -0.545

Therefore, the overall lateral magnification is -0.545.

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Answer:

I'm not that busy solving but I'll tell you the formula that Force x distance is equal to work done

The work is done on a pumpkin when we lift it by 15 m with 24 N is 360 J

Work done is the amount energy gained (loosed) in bringing the body from initial position to final position. It is denoted by W and its SI unit is joule(J).  

i.e. Work(W) is force(F) times displacement(s).

W=F× s

When a body is displaced with 1 newton of force by 1 m, then we can say that work has been done on the body by 1 joule.

Writing for it's dimension,

W=F× s

Force has dimension [L¹ M¹ T²]

Displacement has dimension [L¹]

multiplying both the dimensions Force and Displacement  

we get,

dimension of Work [L² M¹ T²]

According to newton's second law of motion,

Force(F) is mass(M) times acceleration(a).

i.e. F=ma

Given,

Force = 24 N

Displacement = 15 m

W=F.s= 24*15 = 360 J

Hence work done on pumpkin is 360 J

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Answer:

a. 50

Explanation:

You are approximately 5550.6 meters away from the lightning stroke.

To calculate the distance between you and the lightning stroke, we can use the fact that the time it takes for light and sound to reach you is related to their respective speeds.

In this case:

Time for sound to reach you (t_sound) = 16.2 s

Time for light to reach you (t_light) = 0 s (since you see the lightning instantaneously)

Speed of sound (v_sound) = 343 m/s

Speed of light (v_light) = 3 × 10⁸ m/s

Let's first calculate the distance traveled by sound using the formula:

Distance_sound = v_sound * t_sound

Distance_sound = 343 m/s * 16.2 s

Distance_sound = 5550.6 m

Next, let's calculate the distance traveled by light:

Distance_light = v_light * t_light

Distance_light = 3 × 10⁸ m/s * 0 s

Distance_light = 0 m

Since you see the lightning instantaneously, the distance traveled by light is 0.

To find the total distance between you and the lightning stroke, we can add the distances traveled by sound and light:

Total distance = Distance_sound + Distance_light

Total distance = 5550.6 m + 0 m

Total distance = 5550.6 m

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When the bungee cord begins to tighten and your rate of downward acceleration decreases from free-fall to 7.35 m/s², your apparent weight will be greater than your actual weight.

To understand this, let's consider the forces acting on you at that moment. Initially, when you were in free-fall, the only force acting on you was gravity, which caused you to accelerate downward at approximately 9.8 m/s² (acceleration due to gravity on Earth).

However, when the bungee cord starts to tighten, an upward force from the bungee cord comes into play. This force counteracts the downward force of gravity and causes your downward acceleration to decrease.

Apparent weight is the force experienced by an object due to the supporting surface or structure. In this case, your apparent weight is the force exerted on you by the bungee cord, which counteracts the force of gravity and reduces your acceleration.

To calculate your apparent weight, we can use Newton's second law of motion

F_net = m * a

where F_net is the net force, m is your mass, and a is your acceleration.

In this case, the net force is the difference between the downward force of gravity and the upward force from the bungee cord. So we can rewrite the equation as:

F_apparent - m * g = m * a

where F_apparent is your apparent weight, g is the acceleration due to gravity, and a is your reduced downward acceleration.

Solving for F_apparent:

F_apparent = m * (g + a)

Substituting the given values, where a = 7.35 m/s² and g = 9.8 m/s²:

F_apparent = m * (9.8 + 7.35) = m * 17.15

Therefore, at the moment your downward acceleration decreases to 7.35 m/s², your apparent weight will be 17.15 times your actual weight (mg).

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Work Center 40 requires a nominal capacity of 502 hours to complete an order for 500 Z’s when considering both the set-up time and the run time. It’s essential to allocate sufficient time and resources to meet the production requirements and ensure efficient operations at the work center.

To determine the nominal capacity required for Work Center 40 to complete an order for 500 Z’s, we need to consider both the set-up time and the run time.

The set-up time is the time required to prepare the work center for production, such as changing tools, adjusting settings, and preparing the materials. The run time is the actual time it takes to process each unit of the order.

Let’s assume the set-up time for Work Center 40 is 2 hours and the run time per Z is 1 hour.

To calculate the total nominal capacity, we add the set-up time to the product of the run time per unit and the quantity of units in the order:

Nominal capacity = Set-up time + (Run time per Z * Quantity of Z’s)

Nominal capacity = 2 hours + (1 hour/Z * 500 Z’s)

Nominal capacity = 2 hours + 500 hours

Nominal capacity = 502 hours

Therefore, Work Center 40 requires a nominal capacity of 502 hours to complete an order for 500 Z’s when considering both the set-up time and the run time. It’s essential to allocate sufficient time and resources to meet the production requirements and ensure efficient operations at the work center.

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Answer:

Explanation:

The main reason for doing this is to get the attention of the tertiary institutions early. There are thousands of students that apply to these institutions every year, depending on the strictness of the acceptance of these institutions it may or may not be difficult for you to enter. Applying while at grade 11 gives you more chances of getting in as you are catching the attention of the institution and showing a high level of interest. This also allows you more chances to enter, since if you are denied you can try again next year. Aside from this, some institutions have specific requirements, applying early can allow you to know what you are missing as they will tell you if you get denied. You can then work towards obtaining these requirements and apply next year.

Answer:

Two possibities: Increase in pressure or decrease in temperature.

Explanation:

There are two possibilities under the assumption that mass of the gas is conserved and, consquently, the amount of moles is also conserved, a reduction in the volume of the gas leads to an increase in pressure (Boyle's Law) and a decrease in temperature (Gay-Lussac's Law)

The maximum speed the car could round the curve with a reduced coefficient of static friction is approximately 19.8 times the square root of the original coefficient of static friction.

Part A:

The maximum speed at which the car can round the curve without skidding can be determined using the centripetal force equation:

F = (mv^2) / r

Where:

F is the centripetal force,

m is the mass of the car,

v is the velocity of the car, and

r is the radius of the curve.

Since the car is on the verge of skidding out, the centripetal force is equal to the maximum static friction force:

F_friction = μ_s * m * g

Where:

μ_s is the coefficient of static friction,

m is the mass of the car, and

g is the acceleration due to gravity.

Setting these two forces equal, we can solve for the maximum velocity:

(μ_s * m * g) = (m * v²) / r

Rearranging the equation, we can solve for v:

v² = (μ_s * g * r)

Taking the square root of both sides, we find:

v = √(μ_s * g * r)

To find the maximum speed with a reduced coefficient of static friction (μ_s/2), we substitute this value into the equation:

v_max = √((μ_s/2) * g * r)

Calculating the value:

v_max = √((0.5 * μ_s) * g * r)

v_max = √(0.5 * μ_s * 9.8 * 240)

v_max ≈ 19.8 * √(μ_s)

Considering two significant figures, the maximum speed with the reduced coefficient of static friction is approximately 19.8 times the square root of μ_s.

Part B:

Similarly, we can find the maximum speed with an increased coefficient of static friction (2μ_s) using the same equation:

v_max = √((2μ_s) * g * r)

Calculating the value:

v_max = √(2 * μ_s * 9.8 * 240)

v_max ≈ 44.3 * √(μ_s)

Considering two significant figures, the maximum speed with the increased coefficient of static friction is approximately 44.3 times the square root of μ_s.

The maximum speed the car could round the curve with an increased coefficient of static friction is approximately 44.3 times the square root of the original coefficient of static friction.

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The firm will earn maximum total profits if it produces and sells quantity 0b. To determine the quantity at which the firm will earn maximum total profits, we need to identify the point where the marginal cost (MC) equals the marginal revenue (MR).

In the given graph, the MC curve intersects the MR curve at quantity 0b. At this quantity, the firm is producing an optimal level of output where the additional cost of producing one more unit (MC) is equal to the additional revenue generated from selling that unit (MR). This represents the point of profit maximization. Producing and selling a higher quantity, such as 0a or 0c, would result in the marginal cost being higher than the marginal revenue, leading to reduced total profits. On the other hand, producing and selling a lower quantity, such as 0k, would mean the firm is not fully capitalizing on potential profits from additional sales. Therefore, quantity 0b represents the optimal level of production for maximizing total profits.

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Answer:

0.777m

Explanation:

The sound wave has a wavelength of 0.773m.

Explanation:

To solve this problem we have to use the wave equation that is given below:

We know the frequency and the velocity, both of which have good units. All we have to do is rearrange the equation and solve for  

λ :

λ = v f

Let's plug in our given values and see what we get!

λ = 340 m s

440 s − 1

λ = 0.773 m

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The wavelength of the sound wave is 0.662 m.

Explanation:

Given that,

The speed of a sound wave, v = 331 m/s

The frequency of the wave, f = 500 Hz

To find,

The wavelength of the sound wave.

Solution,

The speed of wave in terms of wavelength and frequency is given by :

[tex]v=f\lambda[/tex]

Where

[tex]\lambda[/tex] is the wavelength

Rearranging for [tex]\lambda[/tex],

[tex]\lambda=\dfrac{v}{f}[/tex]

Put all the values,

[tex]\lambda=\dfrac{331}{500}\\\\\lambda=0.662\ m[/tex]

So, the wavelength of the sound wave is 0.662 m.

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Alban Geissler, who developed the SKYRAY carbon fiber wing with Christoph Aarns, suggested after Baumgartner's jump that the wing he used was a copy of two prototype SKYRAY wings sold to Red Bull (Baumgartner's sponsor) two years earlier. - wiki

Explanation:

jouleeeee is the unit kinetic energy is measured in and kinetic energy formula is 1/2mv (square)

Answer:

We're supposed to write a 4-5 paragraph essay for only 6 points...sorry but no

Explanation:

The change in thermal energy of a system is equal to the energy transferred into or out of the system as work, heat, or both.

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed in an isolated system.

Instead, it can only be transferred or converted from one form to another. In the context of thermal energy, this law can be expressed as follows:

ΔU = Q - W

where:

ΔU is the change in internal energy of the system,

Q is the heat transferred into the system, and

W is the work done by the system.

This equation shows that the change in thermal energy of a system is equal to the energy transferred into the system as heat (Q) minus the work done by the system (W).

The first law of thermodynamics is a fundamental principle that describes the conservation of energy in a thermodynamic system.

It states that the change in thermal energy of a system is determined by the net transfer of energy into or out of the system as heat and work.

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1.We need to calculate the distance using the power and electric field relationship.

2.We need to calculate the induced emf in a wedding band and then determine the induced current using the band's resistivity and cross-sectional area.

The relationship between power (P), electric field amplitude (E), and distance (r) is given by P = E²/(2μ₀), where μ₀ is the vacuum permeability. Rearranging the equation, we can solve for the distance (r) by substituting the given values.

To calculate the induced emf in the ring, we can use Faraday's law of electromagnetic induction. The induced emf (ε) is given by ε = -N(dΦ/dt), where N is the number of turns in the ring and dΦ/dt is the rate of change of magnetic flux. By substituting the given values, we can calculate the induced emf.

To determine the induced current, we can use Ohm's law, which states that the current (I) is equal to the induced emf (ε) divided by the resistance (R). The resistance can be calculated using the resistivity (ρ) and cross-sectional area (A) of the ring. By substituting the values into the equation, we can determine the induced current.

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Answer:

the correct one is d  

Explanation:

Let's analyze the situation before reviewing the answers.

When the magnet moves towards the pot, an electromotive force is induced by Faraday's law

         fem =  [tex]- \frac{d \Phi_B }{dt}[/tex] - dfi / dt

         [tex]\Phi_B[/tex] = B . A

In the pot, because it is metallic, a current is created and it is in the opposite direction to the variation of magnetic flux.

By stopping the magnet the flux becomes constant and therefore its derivative is zero, therefore there is no electromotive force and consequently no current.

When reviewing the answers, the correct one is d

An airplane is flying south going 440 mph when it hits a crosswind going west at 35 mph, the resultant velocity of the airplane is approximately 439 mph southwest.

Hence, the correct option is B.

To find the resultant velocity of the airplane, we can use vector addition. The airplane's velocity in the south direction is 440 mph, and the crosswind's velocity in the west direction is 35 mph.

To find the resultant velocity, we can treat the velocities as vectors and add them together. Since the airplane is flying in the south direction and the crosswind is in the west direction, we can consider these vectors as negative in the corresponding directions.

Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as follows

Resultant velocity = [tex]\sqrt{440^{2} }[/tex] + ([tex]-35^{2}[/tex]))

Resultant velocity = 439.66 mph

Since the resultant velocity is directed to the southwest, we can round the magnitude to the nearest mph and the direction to the nearest cardinal direction. Therefore, the resultant velocity of the airplane is approximately 439 mph southwest.

Hence, the correct option is B.

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The total magnetic flux through the plastic of the soda bottle is approximately 0.036 Wb.

To calculate the total magnetic flux through the plastic soda bottle, we need to consider the magnetic field passing through the area of the bottle opening.

The formula for magnetic flux (Φ) is given by

Φ = B * A * cos(θ),

Where B is the magnetic field strength, A is the area, and θ is the angle between the magnetic field and the surface normal.

Given:

B = 1.50 T (magnetic field strength)

d = 3.0 cm (diameter of the bottle opening)

First, we need to calculate the area of the bottle opening. Since the opening is circular, the area can be determined using the formula

A = π * ([tex]r^{2}[/tex]),

Where r is the radius.

r = d/2 = 3.0 cm / 2 = 1.5 cm = 0.015 m

A = π * ([tex]0.015^{2}[/tex]) = 0.00070686 [tex]m^{2}[/tex]

Next, we can calculate the total magnetic flux through the plastic of the soda bottle

Φ = B * A * cos(θ)

θ = 30°

Φ = (1.50 T) * (0.00070686 [tex]m^{2}[/tex]) * cos(30°)

Using a calculator

Φ = 0.036 Wb

Rounded to two significant figures, the total magnetic flux through the plastic of the soda bottle is approximately 0.036 Wb.

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Answer:

22

Explanation:

bc it just is

The answer to the problem can be found using Newton's Third Law, which states that for every action, there is an equal and opposite reaction. When an object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

Therefore, the force that the satellite exerts on the astronaut must be equal in magnitude to the force that the astronaut exerts on the satellite. However, the direction of the force is opposite, i.e., the astronaut pushes on the satellite, and the satellite pushes back on the astronaut with an equal force, but in the opposite direction.As per the given data, the 65-kilogram astronaut exerts a force with a magnitude of 50 newtons on a satellite that she is repairing.

The magnitude of the force that the satellite exerts on her is also 50N. Therefore, the correct answer is 4. 50 N.Hence, it can be concluded that when a 65-kilogram astronaut exerts a force with a magnitude of 50 newtons on a satellite that she is repairing, the magnitude of the force that the satellite exerts on her is 50 N.

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The distance between the first two resonant positions in a resonance tube is One half of the wavelength of the sound wave. Option C

In a resonance tube experiment, the first two resonant positions occur when the length of the tube equals one quarter of the wavelength and then three quarters of the wavelength.

These positions correspond to the first and second resonant frequencies, or harmonics.

Therefore, the distance between these two positions, in other words, the length of the tube at the second resonant position minus the length of the tube at the first resonant position, equals three quarters of the wavelength minus one quarter of the wavelength, which is half a wavelength.

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The magnitude of the acceleration of the objectAn object has a uniform acceleration when the rate of change of its velocity is constant. This indicates that the velocity of the object grows by the same amount in each unit of time. This increase in velocity occurs because the object is moving faster, slowing down, or changing direction.

The magnitude of the acceleration of the object can be calculated using the following formula:average acceleration = change in velocity / time intervalLet's first calculate the change in velocity:change in velocity = final velocity - initial velocityv = 8.0 m/s (final velocity)east - 3.0 m/s (initial velocity)eastchange in velocity = 8.0 m/s - 3.0 m/s = 5.0 m/sThe magnitude of the acceleration of the object can be calculated by inserting the values into the formula:

average acceleration = change in velocity / time intervalaverage acceleration = 5.0 m/s / 2.0 s = 2.5 m/s²Therefore, the magnitude of the acceleration of the object is 2.5 m/s². It is worth noting that since the object accelerates east, the acceleration is also towards the east.

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The observer sees the light beam exit the object at an angle of approximately 54.74° with respect to the x-axis.

What is x-axis and what is denoted on that axis?

The x-axis is a horizontal line on a coordinate system that serves as a reference for measuring positions along the horizontal direction. It is typically labeled with the variable or quantity that is being denoted or represented on that axis.

We have:

Index of refraction outside the object: n₁ = 1 (since it's air)

Index of refraction inside the object: n₂ = 1.2

Angle of incidence: θ_in = 75°

Using Snell's law:

n₁ * sin(θ_in) = n₂ * sin(θ_out)

Substituting the given values:

1 * sin(75°) = 1.2 * sin(θ_out)

To find θ_out, we can isolate it by dividing both sides by 1.2:

sin(θ_out) = (1 * sin(75°)) / 1.2

Using the property that sin(45°) = 1 / √2, we can simplify further:

sin(θ_out) = (1 / √2) / 1.2

Taking the inverse sine (arcsin) of both sides to solve for θ_out:

θ_out = arcsin((1 /√2) / 1.2)

Calculating this value using a calculator, we find that θ_out is approximately 54.74°.

Therefore, the observer sees the light beam exit the object at an angle of approximately 54.74° with respect to the x-axis.

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Answer:

The Right to Protection: According to the Convention, this right includes freedom from all forms of exploitation, abuse and inhuman or degrading treatment.

Explanation:

They by law have to uphold the standards

Answer:

mass of liquid = total mass - mass of container

m = 52000kg - 200kg

m = 519800

D = m/v

D = 519800/160

D = 3,248.75 kgm-³

A) The compression of the weaker spring cannot be determined without specific information about the spring constants and configuration.

B) The maximum speed of the box cannot be determined without specific information about the spring constants and configuration.

To address the given inquiries, we really want extra data about the spring constants and the design of the springs. Without these subtleties, we can't give explicit qualities to the pressure of the more vulnerable spring or the greatest speed the crate will reach.

Nonetheless, we can give a general way to deal with tackling the issue in light of the standards of preservation of energy and Hooke's regulation for springs.

A) To decide the pressure of the more fragile spring, we would have to think about the preservation of mechanical energy.

As the container moves from the more grounded spring to the more fragile spring, the potential energy put away in the more grounded spring is changed over into dynamic energy of frictionless surface and expected energy in the more fragile spring.

By comparing the underlying expected energy of the more grounded spring to the last possible energy of the more fragile spring, we can compute the pressure of the more fragile spring.

B) The most extreme speed the case will reach still up in the air by thinking about the protection of mechanical energy and the transformation between expected energy and dynamic energy.

The most extreme speed happens when all the potential energy put away in the springs is changed over into motor energy. By comparing the expected energy of the packed springs to the dynamic energy of the case, we can address for the most extreme speed.

Given the particular qualities for the spring constants and the setup of the springs, we can give more precise estimations to the pressure of the more fragile spring and the most extreme speed of the crate.

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The magnification of the concave mirror is -0.5. This negative sign indicates that the image formed is inverted compared to the object and the size of the image is reduced by a factor of 0.5 compared to the object.

The magnification (m) of a mirror can be calculated using the formula:

m = -v/u

Where:

m = magnification

v = image distance (distance of the image from the mirror)

u = object distance (distance of the object from the mirror)

Given:

Focal length (f) = -18 cm (negative sign for a concave mirror)

Image distance (v) = -90 cm (negative sign as the image is formed in front of the mirror)

Using the mirror formula, we can determine the object distance (u):

1/f = 1/v - 1/u

Substituting the given values:

1/-18 = 1/-90 - 1/u

Simplifying:

-1/18 = -1/90 - 1/u

Multiply both sides by -18u:

u = 5u - 18

4u = 18

u = 4.5 cm

Now we can calculate the magnification:

m = -v/u

= -(-90) / 4.5

= 90 / 4.5

= -20

Therefore, the magnification of the concave mirror is -0.5.

The magnification of the concave mirror is -0.5. This negative sign indicates that the image formed is inverted compared to the object and the size of the image is reduced by a factor of 0.5 compared to the object.

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I've attached a picture of the 3 electromagnets options below the main electromagnet.

Answer:

The third electromagnet is correct.

Explanation:

From the attached image, in the electromagnet above the 3, we can see that the positive terminal comes before the negative terminal at the bottom left.

Now, when it is reversed, they will both move to the bottom right but their position will change with the negative coming before the positive.

Also, the electric current arrow inside the circle points in the north west direction but when it is reversed, it will point in the north east direction.

Also, the winded coil over the pole remains the same.

Thus, the only option that fulfills this reversed positions is the 3rd electromagnet

Answer:

Explanation:

Its B and C, I got a 5/5 on my test with these answers.