NCERT Physics Class 12 Exemplar Ch 6 Electromagnetic Inductions Part 4
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Q 24. ODBAC is a fixed rectangular conductor of negligible resistance (CO is not connected) and OP is a conductor which rotates clockwise with an angular velocity. The entire system is in a uniform magnetic field B whose direction is along the normal to the surface of the rectangular conductor ABDC. The conductor OP is in electric contact with ABDC. The rotating conductor has a resistance of per unit length. Find the current in the rotating conductor, as it rotates by
Ans:

Between time and the rod OP will make contact with the side BD. Let the length OQ of contact at some t such that be x.

the flux through the area ODQ is
Thus the magnitude of the emf generated is
The current is where R is the resistance of the rod in contact.
For the rod is in contact with the side AB. Let the length of the rod in contact (OQ) be x. The flux through OQBD is B where thus the magnitude of emf generated is
The current is
For the rod will be in touch OC. The Flux through OQABD is
Thus the magnitude of emf
Q 25. Consider an infinitely long wire carrying a current with constant. Find the current produced in the rectangular loop of wire ABCD if its resistance is R.
Ans:
At a distance r from the wire,
Field (out of paper).
Total flux through the loop is
Flux