Electro magnetic induction practice · Mixed difficulty

Two identical coaxial circular loops carry a current $i$ each circulating in the same direction. As the loops are moved away from each other

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

A coil having $\mathrm{500}$ square loops each of side $\mathrm{10}\,\,\mathrm{cm}$ is placed normal to a magnetic field which increases at the rate of $\mathrm{1}\,\,\,\mathrm{W}{\mathrm{m}^{ - 2}}$. The induced emf is

An axle of truck is $\mathrm{2}\mathrm{.5 m}$ long. If the truck is moving due north at $30\,\,m{s^{( - 1)}}$ at a place where the vertical component of the earth’s magnetic field is $90\,\,\mu T$, the potential difference between the two ends of the axle is

A circular coil of area $0.01 \mathrm{~m}^2$ and 40 turns is rotated about its vertical diameter with an angular speed of $50 \mathrm{~rad~s}^{-1}$ in a uniform horizontal magnetic field $0.05 \mathrm{~T}$. If the average power loss due to joule heating is $25 \mathrm{~m W}$. Then, the closed loop resistance of the coil is-

In a dc motor, induced e.m.f. will be maximum

The coil of dynamo is rotating in a magnetic field. The developed induced e.m.f. changes and the number of magnetic lines of force also changes. Which of the following conditions is correct

Assertion: An induced emf appears in any coil in which the current is constant.
Reason: Self induction phenomenon does not obey Faraday's law of induction.

In a uniform magnetic field of induction $B$, a wire in the form of semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is