Two parallel rails with negligible resistance are 13.5 cm apart and are connecte

Question

Two parallel rails with negligible resistance are 13.5 cm apart and are connected by a resistor of resistance R_3 = 5.00 ohm. The circuit also contains two metal rods having resistances of R_1 = 11.5 ohm and R_2 = 15.0 ohm sliding along the rails (see figure). The rods are pulled away from the resistor at constant speeds of v_1 = 4.00 m/s and v_2 = 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 R_3.

Explanation / Answer

Emf generated due to magnetic Field is given by, e = B*l*v

For Left side,
e1 = 0.01 * 0.135 * 4.0
e1 =  0.0054

R1 = 11.5

I1 = e1/(R1+R3)
I1 = 0.0054 / (11.5 + 5)
I1 = 0.000327 A
I1 = 327 uA

Now For Right side,
e2 = 0.01 * 0.135 * 2.0
e2 =  0.0027 v

R2 = 11.5

I2 = -e1/(R2+R3)
I2 = -0.0027 / (15.0 + 5)
I2 = -0.000135 A
I2 = 135 uA

Current through R3, = I1 + I2
Current through R3, = 327 - 135 uA
Current through R3, = 192 uA

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