Max Induced Emf: Homework Statement & Equations

[Fazza3_uae]

Homework Statement

A flat loop of wire of area 15.7 cm² and 1.09 turns is perpendicular to a magnetic field whose magnitude decays in time according to B = 0.5 e^−t/7. What is the maximum induced emf? Answer in units of V.

Homework Equations

$$\epsilon=$$ $$\Delta$$$$\Phi$$_B/$$\Delta$$t


$$\epsilon=$$ - (dB/dt) N A Cos$$\theta$$

The Attempt at a Solution

I have:

A = 15.7 X 10^-4 m²

N = 1.09 turns

B = 0.5 e^-t/7

Maximum $$\epsilon$$ = E _max. = ??


I found E _max. = - ( 1.09) * ( 15.7 X 10^-4 ) * Cos(0) * d(0.5 e^-t/7)/dt

= 1.22 X 10^-4 e^-t/7

Then i found the first deravative of induced emf in terms of time & got another equation.
Then i made that equation equal to zero to find value of time for max. $$\epsilon$$.
But there is no such value for time. Calculator says false everytime which is true.

I tried to take the second deravative and equalize to zero and again same paroblem occured.

Soooo any help will be appreciated.

 

[kuruman]

I found E _max. = - ( 1.09) * ( 15.7 X 10^-4 ) * Cos(0) * d(0.5 e^-t/7)/dt

= 1.22 X 10^-4 e^-t/7

So what is the maximum value of E? More to the point, at what time is the above expression a maximum and what is that maximum value?

 

[Fazza3_uae]

Wow , thanks kuruman for the help , it is right , when time is zero i get a maximum emf E.

but i have a question ,,, can i find the maximum by deravatives and how and when to use ?

thx in advance for all who are helping us ... ^^

 

[kuruman]

You cannot find the maximum by derivatives because the exponential function does not a maximum or minimum. It is either monotonically decreasing or increasing.

 

[Fazza3_uae]

thanks kuruman for eplanation. I understood now why i couldn't find a maximum value when deriving the equation. thanks a lot man .