The bar in the figure falls vertically while maintaining electrical contact with

Question

The bar in the figure falls vertically while maintaining electrical contact with the rails. The rail spacing is 27 cm , and the field strength is B = 1.6 T .(Figure 1)

Part A

If the bar drops from rest, what's the magnitude of the induced emf after it's been falling for 0.4 s ? (You may assume that the magnetic force on the falling bar is much less than the bar's weight.)

Express your answer to one significant figure and include the appropriate units.

Part B

If the bar drops from rest, what's the magnitude of the induced emf after it's been falling for 1.8 s ?

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

Explanation / Answer

here,

magnatic field, B = 1.6 T

rails spacing, d = 27 cm = 0.27 m

Part A:
From Newton Second law, SUM(F)= 0
Fe - Fm = 0 (Fe is electrical Force, Fm = Magnatic field)
Fe = Fm
qE = q*v*B

E = v*B

also ELectrical Field, E = EMF/d

so, EMF = V*d*B -----------------------------(1)

Case:
From First equation of motion Velocity, v = gt = 9.81*0.4 = 3.924 m/s
From Eqn 1 :
EMF = 3.924 * 0.27 * 1.6
EMF = 1.695 J/C

Part B:
From First equation of motion, v = gt = 9.81*1.8 = 17.66 m/s
From Eqn 1 :
EMF = 17.66 * 0.27 * 1.6
EMF = 7.629 J/C

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