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A uniform, steadily increasing magnetic field is confined to a cylindrical region (perpendicular into the page). An equilateral triangular conducting loop is placed so that one vertex coincides with the center of the cylindrical region. The resistances of sides BC and CA are negligible, while side AB has resistance 2 ohm. If the induced current in the loop has magnitude 2 A, find the potential difference between points A and B in volts.

1. 0
2. 2
3. 4
4. 6

Correct answer: 4

Solution

The increasing B induces an EMF in the triangular loop. The two sides BC and CA (zero resistance) together carry the current without any IR drop; the only voltage drop is across AB. By Ohm's law for the AB branch: |V_A - V_B| = I * R_AB = 2 A * 2 ohm = 4 V. This is also equal to the EMF induced in the BC+CA path (since they have no resistance, EMF = V across their terminals). Hence the potential difference between A and B is 4 V.

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