A plane loop is shaped in the form as shown in Fig. 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 for 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
Verified by ExpertsCHECK THE SOLUTION.
Sol. Instantaneous flux through loop is
φ = π a 2 B cos 0º + π b 2 B cos 180º
= π (a 2 – b 2 ) B
= π (a 2 – b 2 ) B 0 sin ω t
Differentiating w.r.t. time,
= π (a 2 – b 2 ) B 0 ω cos ω t
i = 
(only the modulus)
i max = 
, ρ = resistance per unit length
= 
(a – b) B 0 ω
= 
(20 – 10) × 10 2 × 10 × 10 –3 × 
i max = 1 A
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems