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Updated on : 2022-09-05

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Correct option is C)

Ref. image I

Axis of rotation $→$ y-axis.

$B=B(−k^)$

ref. image II

at some time t, area vector makes angle '$θ$' with $B$.

flux, $ϕ=B.A$

$=BAcosθ$

emf, $ε=∣∣∣∣∣ dt−dϕ ∣∣∣∣∣ =(BAsinθdtdθ )$

$=BAωsinθ$

When $θ=2π ,ε=ε_{max}$

So, $θ=nπ+2π $ n = integes

When $θ=0,ε=ε_{min}=0$

So, $θ=nπ$, n = integes

for $ε=ε_{max},θ=ωt=nπ+2π $

$⇒t=ωnπ +2ωπ =(T2π )nπ +2×(T2π )π $

$t=⎝⎜⎜⎛ T2π nπ ⎠⎟⎟⎞ +2(T2π )π $

$=2nT +4T =2n×10 +410 $

$=5n+2.5$

$=2.5s,5+2.5,5×2+2.5...$

$=2.5s,7.5s,12.5s....$

for $ε=ε_{min},θ=ωt=nπ$

$⇒t=ωnπ =(T2π )nπ =2nT $

$⇒t=2n×10 =5n$

$=0s,5s,10s,...$

So, possible option is option (C).

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