Two parallel rails with negligible resistance are 14.0 cm apart and are connecte

Question

Two parallel rails with negligible resistance are 14.0 cm apart and are connected by a resistor of resistance R3 = 5.00 .The circuit also contains two metal rods having resistances of R1 = 10.5 and R2 = 15.0 sliding along the rails (see figure). The rods are pulled away from the resistor at constant speeds of v1 = 4.00 m/sand v2 = 2.00 m/s, respectively. A uniform magnetic field of magnitude B = 0.0100 T is applied perpendicular to the plane of the rails. Determine the current in R3.

______________A

Explanation / Answer

let the rod move a distance dx in dt time

magnetic flux = B*A = B*dx*l

emf = rate of change in flux

E = B*dx/dt*l = B*v*l

aplying Kirchoff law for left loop

E1 = B*v1*l

E1 - I1*R1 - I3*R3 = 0

B*v1*l - I1*R1 - I3*R3 = 0

(0.01*4*0.14)-(I1*10.5)-(I3*5) = 0 ......(1)

for right loop

E2 - I2*R2 +I3*R3 = 0

(0.01*2*0.14)-(I2*15)+(I3*5) = 0 ......(2)

I1 = I2 + I3 .........(3)

I1 = 44 uA

I2 = 250 uA

I3 = 190 uA

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