6th December 2008

JEE Main 2015 Forum › Question Of the Day questions › 6th December 2008

Near Mid-Night question of the day [6]

A wire shpaed as a semi circle of radius a rotates about axis OO' with an angular velocity Ï‰ in a uniform magnetic field of induction B. The rotation axis is perpendicular to the field direction. The total resistance of the circuit is equal to R. Neglecting the magnetic field of the induced current, find the mean amount of thermal power being generated in the loop during a rotation period.

Image in the following post...

**** Edit****
Another one Shamelessly lifted from IE Irodov ;)
*** End Edit ***

#Miscellaneous #Question Of the Day

UP 0 DOWN 0 0 8
Post on FacebookPost anonymously?

8 Answers

62

Lokesh Verma ·2008-12-06 09:09:39

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

satan92 ·2008-12-06 09:17:47

in time t the angle between the B and area= Î¸
Einduced= -d(Ï†b)/dt=-Bd(Acoswt)/dt=BAwsinwt=E₀sinwt

so thermal power= ₀âˆ«^2Ï€/wE₀sinwt*idt
but i= E₀sinwt/R

so total thermal power(after calculating )= (E₀²/2R )T

hence mean thermal power = E₀²/2R

sry forgot to mention E₀=BÏ€a²w/2

UP 0 DOWN 0
Post on FacebookPost anonymously?

62

Lokesh Verma ·2008-12-06 09:38:41

you have made a very small mistake.. in just some constants!!!

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

satan92 ·2008-12-06 09:44:46

not getting that small one!!

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

satan92 ·2008-12-06 09:52:46

please refer to it
not getting the mistake ..

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

Venkatesh Adithya ·2008-12-06 21:05:43

hey area is A/2 since its a semi circle so that's it...

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

satan92 ·2008-12-07 00:39:31

but in my answer A = Ï€a²/2 !!

UP 0 DOWN 0
Post on FacebookPost anonymously?

9

Celestine preetham ·2009-04-29 07:16:23

me too getting same ans as SATAN wats the mistake ?????

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω