Question

ODBAC is a fixed rectangular conductor of negilible resistance (CO is not connnected) and OP is a conductor which rotates clockwise with an angular velocity ω (Fig 6.12). 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 λ per unit length. Find the current in the rotating conductor, as it rotates by 180°.

Answer 1

Between time t = 0 and  t=π/4ω, the rod OP will make contact with the side BD. Let the length OQ of the contact at some time t such that 0<t<π/4ω be x. The flux through the area ODQ is

Thus the magnitude of the emf generated is

The current is I =ɛ/R where R is the resistance of the rod in contact.

For 3π/ω<t <π/ω the rod will be in touch with OC. The Flux through