A rod of length 1.8 m is moving to the right with speed 6.3 m/s along two rails.

Question

A rod of length 1.8 m is moving to the right with speed 6.3 m/s along two rails. Initially, the rod is moving in a region with no magnetic field, but eventually it moves in a region with magnetic field strength 0.64 T pointing out of the page. The rods are connected by a resistor with resistance 82 ? (assume the resistance of the rod and rails is negligible).

1) What is the emf induced by the motion of the rod BEFORE it gets to the magnetic field? e= 0 V

2) What is the emf induced by the motion of the rod IN the magnetic field? e= 7.26 V

3) What is the current induced in the resistor when the rod is moving IN the magnetic field? I= .0885 A

4) What is the force required to keep the rod moving IN the magnetic field? F= ____ N

5) At what rate is mechancial energy delivered to the rod? Prod= ____ W

6) What is the power dissipated by the resistor R? Presistor= ____ W

Explanation / Answer

(1)

the emf induced by the motion of the rod BEFORE it gets to the magnetic field

e = B L v

B is the magnetic field, L is the length of the conductor and v is the velocity of the rod

since B = 0 then e = 0

(2)

  the emf induced by the motion of the rod IN the magnetic fiel

e = B L v

= (0.64) (1.8) (6.3)

= 7.2576 V

(3)

the current induced in the resistor when the rod is moving IN the magnetic field

i = e / R

= 7.2576 / 82

= 0.088 A

(4)

the force on the rod is

F = B i L

= (0.64) (0.088) (1.8)

= 0.101 N

(5)

Prod = F v

= (0.101) (6.3)

= 0.638 W

(6)

Presistor = i2 R

= (0.088)2 (82)

= 0.635 W

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