A closed circuit is formed by a fixed U-shaped conductor and a sliding bar, as s

Question

A closed circuit is formed by a fixed U-shaped conductor and a sliding bar, as shown in the figure. The bar remains in contact with the conductor but is pulled down by gravity. The bar has a mass m = 4.6 grams , a length l = 21 cm , and a resistance R = 0.0018 ? . The U-shaped conductor has a resistance much smaller than this.

The entire circuit is placed in a uniform horizontal magnetic field B= 0.064 T , and the bar allowed to fall. Find the resulting terminal speed of the bar (neglecting air resistance).    

Explanation / Answer

mass of the bar m=4.6g = 4.6*10^-3 kg

length of the bar l=21cm =0.21m

Resistance R=0.0018 ohms= 1.8*10^-3 ohms

mangetic field B=0.064 T

let speed is v

use,

current i=emf/R

i=l*v*B/R

now,

magntic force = weight

i*l*B=m*g

(l*v*B)*l*B/R = m*g

((l*B)^2*v)/R = m*g

(0.21*0.064)^2*v/(1.8*10^-3) = (4.6*10^-3*9.8)

===> v=0.45 m/sec

terminal speed v=0.45 m/sec

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