3) Two long parallel guide wires of zero resistance, separated by a distance d=1

Question

3) Two long parallel guide wires of zero resistance, separated by a distance d=1m, are connected to a potential difference V = 3V. A bar of mass m=12g and resis- tance R = 3 makes contact with these wires, and can slide along them without friction, always remaining perpendicular to the wires. An externally applied uni- form magnetic field B=5T is perpendicular to the plane of the bar and the two wires. Find the velocity of the bar right after 2 seconds, assuming that the bar has an initial velocity of 1.2 m/s at time t-0.

Explanation / Answer

given

d = 1 m ,

V = 3 V

m =12 kg

R = 3 Ohm

B = 5 T

after 2 seconds = t

initial velocity is 1.2 m/s

t = 0

using equation F = m a

m V / t = - | i | d B

m V / t = - d2 B2 V / R

v(t) = v exp ( - d2 B2 t / m R )

= 1.2 X exp ( - 12 X 52 X 2 / 12 X 3 )

v(t) = 0.299 m/s

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