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TFM
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Homework Statement
At the equator, the earth’s magnetic field is approximately horizontal, is directed towards the north and has a value of [tex] 8 × 10^{-5} [/tex] T.
(i)
Estimate the EMF induced between the top and bottom of a bullet shot horizontally at a target on the equator if the bullet is shot east. Assume the bullet has length of 1 cm, a diameter of 0.4 cm and travels at a speed of 300 m/s (for simplicity, one can assume that the bullet has a square cross-section).
Homework Equations
[tex] \epsilon = -\frac{d\Phi}{dt} [/tex]
[tex] \Phi = \int B da = BHx [/tex]
The Attempt at a Solution
I think I have done this question, but would like to check to see it I have done it correctly...
[tex] \Phi = BHx [/tex]
[tex] \epsilon = -\frac{d\Phi}{dt} [/tex]
[tex] \epsilon = -\frac{dBHx}{dt} [/tex]
B and H are constants:
[tex] \epsilon = -BH\frac{dx}{dt} [/tex]
since:
[tex] \frac{dx}{dt} = v [/tex]
[tex] \epsilon = -BHv [/tex]
we know:
B = [tex] 8 × 10^{-5} [/tex]
H = 0.004
v = 300
thus inserting the values I get:
[tex] \epsilon = -9.6 \time 10^{-5} [/tex] Volts
Does this look correct?
TFM