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 lo

Question

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) ${\vec{B}}_{1} = 3 \hat{i} + 7 \hat{j} - 5 t \hat{k}$

(2) ${\vec{B}}_{2} = 5 t \hat{i} - 4 \hat{j} - 15 \hat{k}$

(3) ${\vec{B}}_{3} = 2 \hat{i} - 5 t \hat{j} - 12 \hat{k}$

Where $B$ is in milli tesla and $t$ is in second. If the induced current in the loop due to $\vec{B_{1}}, \vec{B_{2}} \vec{{, B}_{3}}$ are $i_{1}, i_{2}, i_{3}$ respectively then -

TestHub · Accepted Answer

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

Physics - EMI/AC Question with Solution | TestHub

Options:

Doubts & Discussion