A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 100 T.If this wire is pulled to take a square shape in the same plane in 0.1 s,find the average induced EMF in the loop.

Question

dls · Answer

Attempt:
$$\LARGE \phi = BA$$
$$\LARGE \frac{d \phi}{dt}=B \frac{dA}{dt}$$
For change in area..
2 PI r= L (Lets compute in m)
2 pi /10 = L
$$\LARGE L^2=\frac{4 \pi^2}{100}$$ (Final area i.e square's)
Initial Area=>
$$\LARGE \frac{\pi}{100}$$
$$\LARGE e_{induced}=100 \times \frac{\pi (4\pi-1)}{100 \times 0.1}$$
$$\LARGE e_{induced}=10 \pi (4\pi-1) =>363V$$
somehow wrong

ganeshie8 · Answer

how did u get this :
2 PI r= L (Lets compute in m)
2 pi /10 = L

ganeshie8 · Answer

2 PI r  =perimeter of wire right ?

dls · Answer

Perimeter of circle=Perimeter of square :O ?

ganeshie8 · Answer

Is L perimeter of square ?

dls · Answer

oh L/4 ?

ganeshie8 · Answer

yeah, better call L , the side of square

ganeshie8 · Answer

then area of square = L^2

dls · Answer

L is perimeter..then L/4 is side..i.e
length of square side = 2pi/40 
Area of square=>
$$\LARGE Area_{sq}=\frac{4\pi^2}{1600}=>\frac{\pi^2}{400}$$

ganeshie8 · Answer

okie..

ganeshie8 · Answer

hey wait

dls · Answer

Then dA/dt=>
$$\LARGE \frac{dA}{dt}=\frac{\pi}{100}-\frac{\pi^2}{400}=>\frac{\pi}{100}(1-\frac{\pi}{4})$$

dls · Answer

:O

ganeshie8 · Answer

length of square side =  L / 4
                                 =   2 Pi r / 4
                                 = 20 Pi / 4
                                 = 5 pi

ganeshie8 · Answer

right ?

dls · Answer

that is in CM right?

dls · Answer

okay lets do in cm then,
$$\LARGE \frac{dA}{dt}=100\pi-5\pi=95\pi$$

dls · Answer

$$\LARGE e_{induced}=100 \times 95\pi \times 10 =>95000\pi$$
omg

ganeshie8 · Answer

$\LARGE \frac{dA}{dt}=\frac{100\pi-5\pi}{0.1} $

dls · Answer

into 100
wahi to likha

dls · Answer

dA/dt=950 pi

ganeshie8 · Answer

scratch that


$\LARGE \frac{dA}{dt}=\frac{100\pi-(5\pi)^2 }{0.1} $

dls · Answer

emf=950 x 100 = 95000 pi

dls · Answer

lol nvm

dls · Answer

$$\LARGE \frac{dA}{dt}_{final}=>250\pi(4-\pi)$$

dls · Answer

$$\LARGE emf_{Final}=>100 \times 250\pi(4-\pi)=>25000 \pi(4-\pi)$$

dls · Answer

$$\Huge 67510 \times 10^{-4}=>6.75 V$$
Winner!

ganeshie8 · Answer

:) u just missed /4  for L in ur first attempt

dls · Answer

sare physics scientist ab online aa rahe hai -.-

dls · Answer

sigh* yeah :|