Question

A 60 g horizontal metal bar, 15-cm-long, is free to slide up and down between two tall, vertical metal rods that are 15 cm apart. A 5.0×10−2 T magnetic field is directed perpendicular to the plane of the rods. The bar is raised to near the top of the rods, and a 1.2 Ω resistor is connected across the two rods at the top. Then the bar is dropped.

What is the terminal speed at which the bar falls? Assume the bar remains horizontal and in contact with the rods at all times.

Answer 1

SOL)

Given data

Mass of the metal bar, m=60g

Length of the bar, l=15cm

Distance between two vertical metal rod, d=15cm

magnetic field B=5*10^-2 T

Resistance, R=1.2 ohms

Here, gravitational force = magnetic force

m* g=I *l*B   -----(1)

current I =emf /R

I =l*v*B/R   ---(2)

From equation (1) and (2)

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

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

v=60*10^-3*9.8*1.2/(0.15^2*0.05^2)

0.06*11.76/ (0.0225*2.5x10^-3)

0.7056/5.625x10^-5

=12544m/sec      

V=12544 m/sec

Terminal speed, v=12544 m/sec