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In given figure, a wire loop has been bent so that it has three segments ab (a quarter circle), bc (a square corner) & ca (straight line). Here are three choices for a magnetic field through the loop - (1) `vec_(B_(1))=3hati+7hatj-5thatk` (2) `vec(B_(2))=5thati-4hatj-15hatk` (3) `vec(B_(3))=2hati-5thatj-12hatk` 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 thenA. `i_(1)gti_(2)gti_(3)`B. `i_(2)gti_(1)gti_(3)`C. `i_(3)gti_(2)gti_(1)`D. `i_(1)=i_(2)=i_(3)` |
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Answer» Correct Answer - 2 `i_(1)=(dphi_(1))/(dt)(1)/(R)=(d[B_(1)xxArea])/(Rdt)` `=(d)/(dt)[5txx(pia^(2))/(4)]xx(1)/(R)=(5pia^(2))/(4R)` `i_(2)=(dphi_(2))/(dt)xx(1)/(R)=(d[5a^(2)t])/(dt)xx(1)/(R)=(5a^(2))/(R)` `i_(3)=(dphi_(3))/(dt)xx(1)/(R)=(d[0.5a^(2)])/(dt)xx(1)/(R)=(a^(2))/(R)` `thereforei_(2)gti_(1)gti_(3)` |
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