Question

Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 ohm resistor. The circuit also contains two metal rods having resistances of 10.0 ohm and 15.0 ohm sliding along the rails (Fig. P31.31). The rods are pulled away from the resistor at constant speeds of 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 current in the 5.00 ohm resistor.

question taken from physics for scientists and engineers, 6th edition. chapter 31, q.31

Answer 1

$$E_1=Bv_1l=(0.01)(4)(0.1)=0.004\ V\\E_2=Bv_2l=(0.01)(2)(0.1)=0.002\ V\\E=\frac{\frac{0.004}{10}-\frac{0.002}{15}}{\frac{1}{10}+\frac{1}{15}}=0.0016\ V$$

$$I=\frac{0.0016}{6}=0.00027\ A$$