Solve question showing ALL STEPS clearly and using DIAGRAMS Two vertical and two

Question

Solve question showing ALL STEPS clearly and using DIAGRAMS

Two vertical and two horizontal conducting rods are set up as shown in the diagram, with a uniform magnetic field of 58.6 mT pointing into the page. The vertical rods are positioned 5.0 times 10^-2 m apart and the setup has a total resistance of 10 ohm. If just the bottom rod is released, will it fall faster, slower, or at the same speed compared with a similar setup of all insulating rods? Assume all other parameters remain constant. At time t after being released, the rod is falling with a velocity of v = 19.6 m/s. What is the magnitude and direction of the current flowing through the loop? Express the direction as either CW or CCW. What is the current at time t if both horizontal rods are released at the same time? Assume the two rods are identical.

Explanation / Answer

(a) as the bottom rod is falling down, flux through the loop is increasing with time, hence current will induced current in anti clockwise dircetion, to oppose this increamnet in the flux. thus the bottom rod will experience a force, in the opposite dircetion of it's motion( upward direction), hence its speed will decreased,or slower.

(b) emf= induced emf =B*L*V=(58.6 mT )*(5*10^-2)*19.6=0.57 V

i= current= emf/R=0.57/10= 0.057 A , CCW

(c) when both horizental rods are released at same time, then flux through loop will not change with time, that is flux through loop is remains constant. hence induced current is zero.

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