4. [Total: 12 pts] a) [6 pts Consider the electrical circuit shown in Fig. 2(a).

Question

4. [Total: 12 pts] a) [6 pts Consider the electrical circuit shown in Fig. 2(a). There is an infinitely long solenoid (shaded, shown end-on in the Figure). The current arouns that solenoid circulates clockwise and is increasing with time, producing a flux (into the page) that is linear in time: B(t) = at. Surrounding that solenoid are some ideal wires and two resistors, as shown, with ideal voltmeters (that means they have very high internal resistance, and that negligible current flows through them) connected as shown. What do the two voltmeters read (including sign)? How can it be that the two readings are different? Look carefully - shouldn't points a and b have a unique voltage drop between them? If not, why not? b) [6 ptsj Consider the electrical circuit shown in Fig. 2(b). There are two infinitely long solenoid (shaded, shown end-on in the Figure). The solenoids are identical, both with the same cross sectional area of 0.1 m2, and the magnitude of the magnetic field inside both is equal and increasing at a constant rate of 1 T/s. However, note that the direction of the current in the two solenoids, so the B-fields are in fact increasing in opposite directions. The resistors have the values as shown. Determine the current passing through each resistor (magnitude and direction)

Explanation / Answer

First of all the magnetic filed for an ideal infinitely long solenoid is constant inside the solenoid but has no magnectc filed outside the solenoid. So there is no magnetic flux linked with the circuits given here. So no electromagnetic induction hence no current and consequently no voltage drop.  

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