Helicopter in a Magnetic Field - Verticle Component

In summary, a helicopter with a blade span of 10.7m operates in an area with an Earth's magnetic field of 5.85 x 10^-5 T at an angle of 66o to the horizontal. Its rotor blades are moving at 375 rpm in a clockwise direction and this motion causes a voltage difference within them. To answer the given questions, the positive and negative parts of the blades refer to the direction of induced current flow, the vertical component at this point is 2.37 x 10^-5 T, the total flux enclosed in the area swept out by the blades is 0.039 Wb, and the maximum EMF induced in the blades is 5.3277 V.

Homework Statement

A Helicopter with blades that span 10.7m across is operating in an area where the Earth's magnetic field is 5.85 x 10-5T at an angle of 66o to the horizontal. Prior to takeoff the rotor blades are moving at 375rpm in a clockwise direction when viewed from the ground.

It is found that the motion of the blades causes a voltage difference within them.

Helicoper's Blade Span = 10.7 meters
Earth's magnetic field = 5.85 T x 10-5 at angle of 66o to the horizontal

Homework Equations

a) which parts of the rotor blades are positive and negative (don't know what it refers to)
b) Calculate the verticle component at this point
c) Calculate the total flux enclosed in the area swept out by the blades
d) What would be the maximum EMF induced in the blades

The Attempt at a Solution

B)
(sin 24)/ 1 = FV/5.85 x 10-5
FV = (Sin 24) x 5.85x-5
= 2.37 x 10-5

:. The verticle component is 2.37-5

Converted rpm to speed = 210.094 m/s

c)
MAGNETIC FLUX

area of a circle

$\varphi$ = BA
= 2.37 x 10$^{}-5$ x ($\pi$ x 5.35$^{}2$)
= 0.039 WD

d)
V= LvB
= 10.7 x 210.0.94 x 2.37 x 10$^{}-5$
= 5.3277

It it all good?

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I would like to provide some feedback on your solution. Firstly, it is important to clarify what is meant by "positive and negative" parts of the rotor blades. It is most likely referring to the direction of the induced current flow in the blades. As the blades are rotating clockwise, the induced current will flow from the top of the blades to the bottom, making the top the positive end and the bottom the negative end.

Next, for part b) calculating the vertical component, you have correctly used the equation FV = (sin 24) x 5.85 x 10^-5. However, the units for this should be Tesla (T), not just 10^-5. So the final answer should be 2.37 x 10^-5 T.

For part c), you have correctly calculated the magnetic flux, but your units are incorrect. The unit for magnetic flux is Weber (Wb), not WD. So the final answer should be 0.039 Wb.

For part d), you have correctly used the equation V = LvB to calculate the maximum EMF induced in the blades. However, the units for this should be volts (V), not just 10^-5. So the final answer should be 5.3277 V.

Overall, your solution is on the right track but it is important to pay attention to units and clarify any ambiguous terms. Good job!

1. How does a helicopter fly in a magnetic field?

A helicopter is able to fly in a magnetic field due to the presence of a vertical component in the field. This component causes a force known as the Lorentz force to act on the helicopter's blades, which allows it to lift off and maneuver.

2. What is the purpose of the vertical component in a magnetic field for a helicopter?

The vertical component in a magnetic field is essential for a helicopter as it allows for the generation of lift through the Lorentz force. Without this component, a helicopter would not be able to fly in a magnetic field.

3. Can a helicopter fly in any type of magnetic field?

As long as there is a vertical component present, a helicopter can fly in a magnetic field. However, certain types of magnetic fields, such as those with high levels of interference, can make it more difficult for a helicopter to fly safely.

4. How does the strength of the magnetic field affect a helicopter's flight?

The strength of the magnetic field can affect a helicopter's flight in a number of ways. A stronger magnetic field can result in a greater Lorentz force acting on the blades, which can increase lift and affect the helicopter's stability.

5. Are there any safety concerns with flying a helicopter in a magnetic field?

There can be safety concerns when flying a helicopter in a magnetic field, particularly if the field is strong or has high levels of interference. This can affect the helicopter's flight and navigation systems, so it is important for pilots to be aware of these potential hazards.

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