# (a) A conductor of length ‘l’ is rotated about one of its ends at a constant angular speed in a plane perpendicular to a uniform magnetic field B. Plot graphs to show variations of the emf induced across the ends of the conductor with     (i) angular speed and         (ii) length of the conductor l.(b) Two concentric circular loops of radius 1 cm and 20 cm are placed coaxially.     (i) Find mutual inductance of the arrangement.     (ii) If the current passed through the outer loop is changed at a rate of 5 A/ms, find the emf induced in the inner loop. Assume the magnetic field on the inner loop to be uniform.

a)

$\text{e.m.f. induced in the rod}=|\frac{-d\phi}{dt}|$

$e=\frac{1}{2}Bl^2\omega$

i)

ii)

i) Imagine a current I to flow through the larger coil. Magnetic flux linked with the smaller coil = MI

$=\frac{\mu_0I}{2\pi r}\times \pi\times10^{-4}\\\\implies\ M=\frac{\mu_0\pi\times10^{-3}}{4}=10^{-9}H$

ii)

$e=-M\frac{di}{dt}$

$\\=-10^{-9}\times\frac{5}{10^{-3}}V\\=-5\times10^{-6}V$

a)

$\text{e.m.f. induced in the rod}=|\frac{-d\phi}{dt}|$

$e=\frac{1}{2}Bl^2\omega$

i)

ii)

i) Imagine a current I to flow through the larger coil. Magnetic flux linked with the smaller coil = MI

$=\frac{\mu_0I}{2\pi r}\times \pi\times10^{-4}\\\\implies\ M=\frac{\mu_0\pi\times10^{-3}}{4}=10^{-9}H$

ii)

$e=-M\frac{di}{dt}$

$\\=-10^{-9}\times\frac{5}{10^{-3}}V\\=-5\times10^{-6}V$

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