(a) Redraw the set-up and show the direction of the Earths magnetic field inside

Question

(a) Redraw the set-up and show the direction of the Earths magnetic field inside

the loop, including the angle given above. (Assume that the North pole of a

compass, which is held parallel to the ground points to the right).

(b) The horses can pull the sliding rail at 10 miles per hour. How large is the

voltage generated across the leads to the TV? How much current flows in the

circuit? Indicate the current direction on the diagram.

(c) What is the magnetic force on the sliding rail? Indicate the direction on the

diagram.

(d) How much power is expended by the horses? How much electrical power

does the TV use?

(e) The farmer is probably not very impressed by the numbers. She therefore

considers different ways to improve the set up in order to reach a voltage of

120 V. She asks for your help on each of the following ideas:

-She wants to let her horses run back and forth (with the same

maximum pulling speed). Would this increase the induced voltage

difference? Would a steady voltage be generated (why/why not)?

- She wants to buy new horses which can pull faster. How fast would

these new horses have to pull to generate the desired 120 V (keeping

the other parameters as before)? Is this speed feasible?

(f) Finally, instead of the linear idea above, the trainer hooks up the horses via a

frictionless gearing mechanism to a wire coil (see figure). The coil has 100 turns and

an area of 0.2 m2, and it sits inside a permanent magnet that provides a constant field

of 0.01 T. The coil turns such that it flips between parallel and perpendicular to the

magnetic field at each quarter-turn. The horses now pull on the gear chain, which

causes the coil to go through 10 complete rotations for each meter the horses run. How

fast do the horses have to run to generate an average voltage of 120V? (Note that the

Explanation / Answer

a)

b)

V = B L v cos(90 - 70) = 5.5e-5 * 25 * (10 * 0.44704) * cos20 = 5.78 x 10^-3 V

i = V/R = 0.0057761/10 = 5.78 x 10^-4 A

c)

We must find total magnetic force (and therefore we dont use sin or cos)

F = B L i = 5.5e-5 * 25 * 5.78e-4 = 7.94 x 10^-7 N

Direction:

d)

P = F v = 7.94x10^-7 * (10 * 0.44704) = 3.55 x10^-6 W

P_TV = 3.55 x 10^-6 W

e)

- No, it will not change.

- No, as the horses run back and forth the induced current will change.

V = B L v cos(90 - 70) ==> v = V/(B L cos20) = 120/(5.5e-5 * 25 * cos20) = 92874 m/s

- No, this speed is not feasible.

f)

V_mean = (2/pi) V_max

==> V_max = pi/2 V_mean = 3.1416/2 * 120 = 188.5 V

V_max = N A B w

==> w = V_max/(N A B) = 188.5/(100*0.2*0.01) = 942.5 rad/s

==> f = w/2pi = 942.5/2/3.1416 = 150 Hz

10 complete rotations takes "t" seconds: t = 10/150 = 0.06667 s

==> v = x/t = 1/0.06667 = 15 m/s

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