A conducting circular loop is placed in a uniform magnetic field of $$0.04\ T$$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $$2\ mm/s$$. The induced emf in the loop when the radius is $$2\ cm$$ is
Induced emf in the loop is given by
$$e = -B . \dfrac {dA}{dt}$$ where $$A$$ is the area of the loop.
$$e = -B.\dfrac {d}{dt}(\pi r^{2}) = -B\pi 2r \dfrac {dr}{dt}$$
$$r = 2\ cm = 2\times 10^{-2} m$$
$$dr = 2\ mm = 2\times 10^{-3}m$$
$$dt = 1s$$
$$e = -0.04\times 3.14\times 2\times 2\times 10^{-2} \times \dfrac {2\times 10^{-3}}{1}V$$
$$= 0.32\pi \times 10^{-5}V$$
$$= 3.2\pi \times 10^{-6}V$$
$$= 3.2\pi \mu V$$.
At the centre of a fixed large circular coil of radius $$R$$, a much smaller circular coil of radius $$r$$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $$I$$. The smaller coil is set to rotate with a constant angular velocity $$\omega$$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $$t$$ of its start of rotation.
A small circle loop of wire of radius a is located at the centre of a much larger circular wire loop of radius $$b$$. The two loops are in the same plane. The outer loop of radius $$b$$ carries an alternating current $$ I + I_o cos (\omega \,t) $$ . The emf induced in the smaller inner loop is nearly :
A conducting square loop is placed in a magnetic field $$B$$ with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate $$\alpha$$/ The induced emf in the loop at an instant when its side is $$'a'$$ is
For $$MRI$$, a patient is slowly pushed in a time of $$10\ s$$ within the coils of the magnet where magnetic field is $$B = 2.0\ T$$. If the patient's trunk is $$0.8\ m$$ in circumference, the induced emf around the patient's trunk is
A square current carrying loop is changed to a circular loop in time $$t_{1}$$. Then
A conducting wire in the form of circular loop of radius $$\sqrt{\displaystyle\frac{2}{\pi}}$$m is places normal to a uniform magnetic field of induction 2T. If the magnetic induction is uniformly reduced to T in 2s, the induced e.m.f in the loop is ____________.
A square-shaped copper coil has edges of length $$50\, cm$$ and contains $$50$$ turns. It is placed perpendicular to a $$1.0\, T$$ magnetic field. It is removed from the magnetic field in $$0.25\, s$$ and restored in its original place in the next $$0.25\, s$$. Find the magnitude of the average emf induced in the loop during (a) its removal, (b) its restoration and (c) its motion.
The current in a solenoid of $$240$$ turns, having a length of $$12 cm$$ and a radius of $$2 cm$$, changes at a rate of $$0.8 A s^{-1}$$. Find the emf induced in it.
A conducting circular loop of area $$1m{m}^{2}$$ is placed coplanarly with a long, straight wire at distance of $$20cm$$ from it. The straight wire carries an electric current which changes from $$10A$$ to zero in $$0.1s$$. Find the average emf induced in the loop in $$0.1s$$.
A copper wire having a resistance of $$0.01$$ ohm in each metre is used to wind a $$400$$ turn solenoid of radius $$1.0\ cm$$ and length $$20\ cm$$. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of $$1.0 \times 10^{-2}$$ T near the centre of the solenoid.