A plane loop is shaped in the form as shown in figure with radii a = 20 cm and b = 10 cm and is placed in a uniform time varying magnetic field B = B 0 sin ω t, where B 0 = 10 mT and ω = 100 rad/s. Find the amplitude of the current induced in the loop if its resistance per unit length is equal to 50 × 10 –3 Ω /m. The inductance of the loop is negligible
Text Solution
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( 0001)
Sol. Instantaneous flux
= π a 2 B cos0° + π b 2 B cos180°
= π (a 2 – b 2 ) B
φ = π( a 2 – b 2 ) B 0 sin ω t
λ = 
i = 
i = 
R = ρ × 2 π (a + b)
∴ i max = 
= 1 Amp
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