In the accompanying diagram, a pair of conducting rails supports the red bar, le

Question

In the accompanying diagram, a pair of conducting rails supports the red bar, length l = 40 cm, which is pulled downward by gravity at a constant terminal speed of vT = 5 m/s. If there is a magnetic field out of the page with a strength B0 = 1 T, and the resistance is R = 2 ohm, what are the induced emf e0 and the induced current I0 in the loop ( both magnitude and direction)? What is the power PR dissipated by the resistor? What is the magnetic force FB on the red bar (magnitude and direction)? What is the mass M of the bar needed to maintain this terminal speed?

Explanation / Answer

here ,

a)

induced EMF = B*v*L

induced EMF = 1* 5 * 0.40

induced EMF = 2 V

the induced emf is 2 V

induced current = induced EMF/R

induced current = 2/2

induced current = 1 A

the induced current is 1 A

as the flux through the loop is increasing , according to Lenz law ,

the direction of induced current is CLOCKWISE

b)

power = I^2 * R

Power = 1^2 * 2

Power = 2 W

the power dissipated is 2 W

c)

Fa = B*I*L

Fa = 1 * (1) * 0.40

Fa = 0.40 N in the direction oposite to velocity

d)

for terminal speed ,

Fa = m*g

0.40 = m*9.8

m = 0.0408 Kg = 40.8 gm

the mass of rod is 40.8 gm

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