A metal rod of resistance 20 Ω is fixed along a diameter of a conducting ring of radius 0 . 1 m and lies on x - y plane. There is a magnetic field B → = ( 50 T ) k ^ . The ring rotates with an angular

Question

A metal rod of resistance 20 Ω is fixed along a diameter of a conducting ring of radius 0 . 1 m and lies on x - y plane. There is a magnetic field B → = ( 50 T ) k ^ . The ring rotates with an angular velocity ω = 20 r a d s - 1 about its axis. An external resistance of 10 Ω is connected across the centre of the ring and rim. The current through external resistance is

TestHub · Accepted Answer

Here, resistance of rod = 2 Ω , r = 0.1 m , B = 50 T , a l o n g z - a x i s ω = 20 r a d s - 1 . Potential difference between centre of the ring and the rim is V = 1 2 B ω r 2 = 1 2 × 50 × 20 × 0.1 2 = 5 V Current through external resistance, i = E R + r = 5 10 + 5 = 1 3 A

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