- #1

- 3

- 0

In preparation for an upcoming physics exam I have been going through some past paper questions. This question is from the multiple choice section of the paper, so while I can check the answer there is no source from which I can see it being worked through.

An aircraft of wing span 60m flies horizontally at a speed of 150 ms^-1. If the vertical component of the Earth's magnetic field is 1.0 * 10^-5 T, what emf is induced across the wing tips of the plane?

radius of Earth = 6.37 * 10^6 m

[tex]F = Bqv[/tex]

[tex]F = BIlsin(\theta)[/tex]

[tex]\Phi = BAcos(\theta)[/tex]

[tex]\epsilon = N \frac{Δ\Phi}{Δt} [/tex]

[tex]\epsilon = BANωsin(ωt)[/tex]

I know the length of the conductor, its velocity, and the relevant magnetic flux density.

If [itex]F = Bqv[/itex] and [itex]F = BIl[/itex], then [itex]\frac{Il}{qv} = 1[/itex]

as [itex]q = It[/itex], [itex]\frac{l}{tv} = 1[/itex], so [itex]t = \frac{l}{v}[/itex]

substituting in the values given for v and l gives t as [itex] 0.4s [/itex]

This seems intuitively wrong, but I can't think of anything else to do.

I also know the radius of the Earth, so I can find an angular velocity for the aircraft. This comes out as about [itex] 2.35 * 10^{-5} s^{-1} [/itex].

I'm not sure what to do about the area term in the equations.

Anyone care to give some advice?

## Homework Statement

An aircraft of wing span 60m flies horizontally at a speed of 150 ms^-1. If the vertical component of the Earth's magnetic field is 1.0 * 10^-5 T, what emf is induced across the wing tips of the plane?

radius of Earth = 6.37 * 10^6 m

## Homework Equations

[tex]F = Bqv[/tex]

[tex]F = BIlsin(\theta)[/tex]

[tex]\Phi = BAcos(\theta)[/tex]

[tex]\epsilon = N \frac{Δ\Phi}{Δt} [/tex]

[tex]\epsilon = BANωsin(ωt)[/tex]

## The Attempt at a Solution

I know the length of the conductor, its velocity, and the relevant magnetic flux density.

If [itex]F = Bqv[/itex] and [itex]F = BIl[/itex], then [itex]\frac{Il}{qv} = 1[/itex]

as [itex]q = It[/itex], [itex]\frac{l}{tv} = 1[/itex], so [itex]t = \frac{l}{v}[/itex]

substituting in the values given for v and l gives t as [itex] 0.4s [/itex]

This seems intuitively wrong, but I can't think of anything else to do.

I also know the radius of the Earth, so I can find an angular velocity for the aircraft. This comes out as about [itex] 2.35 * 10^{-5} s^{-1} [/itex].

I'm not sure what to do about the area term in the equations.

Anyone care to give some advice?

Last edited: