91影视

i) Area of the loop $A=0.15m^2$

ii) Magnetic field$B=0.20T$

iii) Angle$胃=\frac{蟺}{2}rad=90掳$

iv) Angular speed$蝇=0.60rad/s$

Use Faraday鈥檚 law to find the emf induced in the coil. Substituting the expression of the flux in the emf and substituting all the given values, find the required value of the induced emf.

Faraday'slaw of electromagnetic inductionstates, Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced in it.

Formulae are as follows:

$蔚=-\frac{d蠒}{dt}$

$蠒=\stackrel{鈫�}{B}.\stackrel{鈫�}{A}$

Where,$蠒$is magnetic flux, B is magnetic field, A is area, 饾渶 is emf.

Since, the loop is rotating continuously in the uniform magnetic field, the magnetic flux through the loop changes.

And this flux is given by,

$f=\stackrel{鈫�}{B}.\stackrel{鈫�}{A}=BA\cos 胃$

The rate of change of the flux is nothing but the emf induced and by Faraday鈥檚 law, it is given by,

$蔚=-\frac{d蠒}{dt}$

Where the negative sign shows that the magnetic field due to the currentopposes the change in the magnetic flux that induces the current.

Substituting the flux in Faraday鈥檚 law,

$蔚=-\frac{d}{dt}(BA\cos 胃)$

$蔚=BA\sin 胃\frac{d胃}{dt}$

Since,$B=0.20T,A=0.15m^2,蝇=\frac{d胃}{dt}=0.60\frac{rad}{s}$

Substituting all the values,

$蔚=0.20T脳0.15m^2脳sin{90}^0脳0.60\frac{rad}{s}$

$蔚=0.018V$

Hence, the emf induced in the loop is 0.018 V.

Therefore, using Faraday鈥檚 law, the emf induced in the coil can be determined.