A uniform magnetic field is present in a cylindrical region as shown. This field is increasing uniformly with time. An equilateral loop is placed in such a way that its vertex coincide with centre of

Question

A uniform magnetic field is present in a cylindrical region as shown. This field is increasing uniformly with time. An equilateral loop is placed in such a way that its vertex coincide with centre of cylindrical region. Resistances of sides BC and CA are negligible whereas that of AB is $2Ω$ . If a current of magnitude 2 A ampere flows in the triangular loop, due to induced emf, find potential difference between points A and B (in volt).

TestHub · Accepted Answer

The induced electric field is azimuthal about the centre O. The vertex of the loop coincides with O, so the two sides through O are radial and carry zero induced emf; the whole emf $E$ appears along AB.

Loop current: $E = I R_{A B} = 2 \times 2 = 4$ V.

Potential difference between A and B: $V_{A} - V_{B} = I R_{A B} - E_{A B}$

$= 4 - 4 = 0$ V.

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