Figure shows a conducting rod of negligible resistance that can slide on smooth U-shaped rail made of wire of resistance 1 Ω /m. position of the conducting rod at t = 0 is shown. A time t dependent magnetic field B = 2t tesla is switched on at t = 0
(i) The current in the loop at t = 0 due to induced emf is –
Text Solution
Verified by Experts(i) Sol; (ii) Sol; (iii) Sol
Ans.
(i)
Sol. 
= 2T/s
E = – 
= – 800 × 10 –4 m 2 × 2 = – 0.16 V
i = 
= 0.16 A, clockwise
(ii)
Sol. At t = 2s, B = 4T, 
2T/s
A = 20 × 30 cm 2 = 600 × 10
–4 m 2 ; 
–(5 × 20) cm 2 /s
= – 100 × 10 –4 m 2 /s
= – [4 × (– 100 × 10 –4 ) + 600 × 10 –4 × 2]
= – [–0.04 + 0.120] = – 0.08 v
(iii)
Sol. At t = 2s, length of the wire
= (2 × 30 cm) + 20 cm = 0.8 m
Resistance of the wire = 0.8 Ω
Current through the rod 
A
Force on the wire = ilB = 
× (0.2) × 4 = 0.08 N
same force is applied on the rod in opposite direction to make net force zero.
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