1). A metal rod lies across frictionless parallel rails in a uniform magnetic fi

Question

1).
A metal rod lies across frictionless parallel rails in a uniform magnetic field that points normal to the plane of the rails. The rails are connected at one end, but not the other, so that a current can pass through the rod. The rod moves to the right at speed v, so that the area enclosed by the current loop is increasing. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should
Choose one answer.
A. not change
B. increase linearly with time
C. decrease linearly with time
D. increase quadratically with time
E. decrease quadratically with time

2).

One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.100 m2. The circuit is completed by connecting the coil to a 10O resistor. The magnetic field along the coil axis is made to change from 1.00T in one direction to 1.00T in the other direction. What is the total charge that flows through the resistor in this process?

(Note that the question asks for charge, not current. Be sure to enter the correct units.)

Explanation / Answer

(1) In order for the emf around the circuit to be zero, the magnitude of the magnetic field should sholud be constant (Not changes) thus, option : A is correct (2) Area of the cross-section of the iron core : A = 0.1 m2 NO, of turns = N = 100 change in magnetic field : d B = 1 T -(- 1 T) = 2 T It is known by the formula for induced emf : emf :  E = N A dB /dt Current : I = E/ R =  (N A/R) [dB /dt ]                  thus, charge : Q = I dt = N A dB / R                                                    = (100)(0.1)(2)/(10)                                                    = 2 coulumbs

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