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

$A$ circular coil of radius $10\, cm$ is placed in a uniform magnetic field of $3.0 \times 10^{-5}\, T$ with its plane perpendicular to the field initially. It is rotated at a constant angular speed about an axis along the diameter of the coil and perpendicular to the magnetic field so that it undergoes half a rotation in $0.2\, s$. The maximum value of $EMF$ induced (in $\mu V$) in the coil will be close to the integer $....\mu V$.

$A$ ring of resistance $10 \ \Omega$,radius $10 \ cm$ and $100$ turns is rotated at a rate of $100$ revolutions per second about its diameter perpendicular to a uniform magnetic field of induction $10 \ mT$. The amplitude of the current in the loop will be nearly $....... \ A$. (Take: $\pi^2 = 10$)

$A$ student pedals a stationary bicycle. The pedals of the bicycle are attached to a $100$ turn coil of area $0.10$ $m^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01$ $T$ perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil (in $V$)?

$A$ ring of resistance $10 \Omega$,radius $10 \text{ cm}$,and $100$ turns is rotated at a rate of $100$ revolutions per second about a fixed axis which is perpendicular to a uniform magnetic field of induction $10 \text{ mT}$. The amplitude of the current in the loop will be nearly $A$ (Take $\pi^2 = 10$).

The phase difference between the magnetic flux linked with a coil rotating in a uniform magnetic field and the induced $e.m.f.$ produced in it is