Helicopter in a Magnetic Field - Verticle Component

[miniradman]

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 66^o 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 66^o to the horizontal
Rate of blades = 375rpm

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?

 

[anathema]

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!