NTA Abhyas JEE Main2020PhysicsElectromagnetic InductionPractice
In given figure, a wire loop has been bent so that it has three segments a b (a quarter circle), b c (a square corner) & c a (straight line). Here are three choices for a magnetic field through the loop - (1) B → 1 = 3 i ^ + 7 j ^ – 5 t k ^ (2) B → 2 = 5 t i ^ – 4 j ^ – 15 k ^ (3) B → 3 = 2 i ^ – 5 t j ^ – 12 k ^ Where B is in milli tesla and t is in second. If the induced current in the loop due to B 1 → , B 2 → , B
Options
- Ai 1 > i 2 > i 3
- Bi 2 > i 1 > i 3
- Ci 3 > i 2 > i 1
- Di 1 = i 2 = i 3
Correct answer
B. i 2 > i 1 > i 3
Step-by-step solution
i 1 = d ϕ 1 d t 1 R = d B 1 × A r e a R d t = d d t 5 t × π a 2 4 × 1 R = 5 π a 2 4 R i 2 = d ϕ 2 d t × 1 R = d 5 a 2 t d t × 1 R = 5 a 2 R i 3 = d ϕ 3 d t × 1 R = d 0.5 a 2 d t × 1 R = a 2 2 R ∴ i 2 > i 1 > i 3