Suppose you install a compass on the center of a car\'s dashboard. (a) Assuming

Question

Suppose you install a compass on the center of a car's dashboard.

(a) Assuming the dashboard is made mostly of plastic, compute an order-of-magnitude estimate for the magnetic field at this location produced by the current when you switch on the car's headlights. (Suppose you have two 104-W headlights running in series from a 12-V battery with all the current going through the switch 62 cm from the compass. Model the current as being from a long straight wire.)

10-110-3    10-610-910-12

(b) How does this estimate compare with the Earth's magnetic field?

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Explanation / Answer

First, P = IV

208 = I(12)

I = 17.3 Amps

Then B = uI/2pi(r)

B = (4pi X 10-7)(17.3)/(2pi)(.62)

B = 5.58 X 10-6 T

Thus the order of magnitude is in the 10-6 range (That is .000001)

Part B

The is one order of magnitude less than the Earth's B field.

That means the Earth's B field is 10 times stronger.

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