# Maximum Induced Emf

1. Nov 27, 2009

### Fazza3_uae

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

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

3. 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.

2. Nov 27, 2009

### kuruman

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?

Last edited: Nov 27, 2009
3. Nov 27, 2009

### Fazza3_uae

Wow , thx 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 ... ^^

4. Nov 27, 2009

### 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.

5. Nov 28, 2009

### 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 .