You\'re an electrical engineer designing an alternator (the generator that charg

Question

You're an electrical engineer designing an alternator (the generator that charges a car's battery). Mechanical engineers specify a 10-cm-diameter rotating coil, and you determine that you can fit 250 turns in this coil. To charge a 12-Vbattery, you need a peak output of 17 V when the alternator is rotating at 1000 rpm.

What do you specify for the alternator's magnetic field? HINT: Notice that the rotation rate of the coil is given in revs per minutes, not revs per second.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given

d = 10 cm = 0.1 m

V_peak = 17 volts

n = 250 turns

w = 1000 rpm = 1000*2*pi/60 = 104.7 rad/s

Area of the loop, A = pi*d^2/4 = pi*0.1^2/4 = 0.0785 m^2

let B is the requiredmagnetic field.
V_peak = N*A*B*w

==> B = V_peak/(N*A*w)

= 17/(250*0.00785*104.7)

= 0.083 T

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