Q16: Two parallel rails with negligible resistance are 13.0 cm apart and are con

Question

Q16:

Two parallel rails with negligible resistance are 13.0 cm apart and are connected by a resistor of resistance

R3 = 5.00 ?.

The circuit also contains two metal rods having resistances of

R1 = 14.0 ?

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/s

and

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

---Select---

upward

downward

to the left

to the right

no direction

Explanation / Answer

in left loop :

Bv1 - I2R2 - I1R1 = 0

in right loop

Bv3 - I3R3 + I1R1 = 0

at junction I2 = I1 + I3

I1 = Bd[(v1R2 - v2R1)/(R1R2 + R1R3 + R2R3) ] (upwards)

B = 0.0100 T ; d = 13 cm = 13 x 10^-2 m

v1 = 4 m/s ; v2 = 2 m/s ;

R1 = 14 ; R2 = 15 ; R3 = 5

I1 = 1.17 x 10^-4 A = 117 micro A upwards

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