A wire of mass 59 g slides without friction on two horizontal conducting rais sp

Question

A wire of mass 59 g slides without friction on two horizontal conducting rais spaced 0.8 m apart. A steady current of 100 A is in the circuit formed by the wire and the rails. A uniform magnetic field of 1.5 T, directed into the plane of the drawing, acts on it Wire Bin 0.8 m (a) In which direction in the figure above will the wire accelerate? left o right into the page o out of the page O The magnitude of the acceleration is zero (b) What is the magnetic force on the wire? (Give the magnitude only.) (c) How long must the rails be if the wire, starting from rest, is to reach a speed of 200 m/s? (d) If the mognetic field were directed out of the page, how would your answers differ? O The directions of the force and the acceleration would remain the same, but their magnitudes would be significantly reduced The directions of the force and the acceleration would remain the same, but their magnitudes would double. O The force on the wire duc to the magnetic ficld would point to the left and the wire would accclerate in that direction. The numerical values would remain the same, though. The force on the wire due to the magnetic field would point to the right and the wire would accelerate in that direction. The numerical values would remain the same, though. (e) What the magnetic field were directed toward the top of the drawing? The force on the wire due to the magnetic field would be equal to zero because the current and magnetic field would be antiparallel. O There would be no change. The force on the wire and consequentially the acceleration of the wire would both reverse in direction with magnitudes unchanged. The force on the wire and consoquentially the acceleration of the wire would increase significantly in magnitude, but their directions would remain unchanged.

Explanation / Answer

a) F = I ( L x B )

L is downwards and B is into the page

F = towards rigt

b) F = 100 x 0.8 x 1.5 = 120 N

c) a = F/m = 120 / 0.059 = 2033.89 m/s^2

using v^2 - u^2 = 2ad

200^2 - 0 = 2 x 2033.89 x d

d = 9.83 m

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