Consider a set of conducting metal tracks (two parallel beams with a flat top su
ID: 1316547 • Letter: C
Question
Consider a set of conducting metal tracks (two parallel beams with a flat top surface) 0.3 m apart. Across the tracks, perpendicular to them, is a conducting rod of mass 0.65 kg. There is a uniform magnetic field of 0.80 T directed into the page. [A Tesla is the SI unit of magnetic fi eld strength, 1 T = 1 N / (A m).] A circuit consisting of a 47 Ohm resistor and a 15 V power supply is placed across the rails. What is the acceleration of the rod?
Hint: First calculate the current (Ohm's law), then then force on the rod and finally the acceleration (Newton's 2nd law).
Explanation / Answer
power delivered by the battey = V^2/R = 15^2/47 = 4.79 Watts
let v is the speed of the rod
magnetic force on rod, F = B*v*L*sin(90)
= 0.8*v*0.3*1
= 0.24*v
power required to move the rod with speed
P = F*v
power deliverd by the battery = power required to move the rod
4.79 = F*v
4.79 = 0.24*v*v
v^2 = 4.79/0.24
==> v = sqrt(4.79/0.024)
= 4.47 m/s <<<<<<<<<<<<<<------------Answer