Two parallel rails with negligible resistance are 14.5 cm apart and are connecte

Question

Two parallel rails with negligible resistance are 14.5 cm apart and are connected by a 5.00 Ohm resistor. The circuit also contains two metal rods having resistances of R = 10.0 ? and 15.0 ? sliding along the rails. The rods are pulled away from the resistor at constant speeds 4.00 m/s and 2.00 m/s, respectively. A uniform magnetic field of magnitude 0.0100 T is applied perpendicular to the plane of the rails. Determine the magnitude and direction of the current in the 5.00 ? resistor. Your response differs from the correct answer by more than 10%. Double check your calculations. muA

Explanation / Answer

?flux = BA

dflux/dt = BdA/dt as field is constant .


E1 = BdA/dt = (0.01)(0.145)x4 = 5.8 mV

E2 = 0.01x0.145x2 = 2.9 mV

now let i1 and i2 are current in circuit due to E1 and E2

now in 5.0 ohm current is i1 - i2

10i1 + 5(i1 -i2) = 5.8 m

15 i2 - 5(i1 -i2) = 2.9 m

i1 = .4745 mA

i2 = .263636 mA

current in 5 ohm = i1 - i2 =0.210864 mA = 210.864 ?A

direction is bottom to top

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