$A$ rod of $10 \ cm$ length is moving perpendicular to a uniform magnetic field of intensity $5 \times 10^{-4} \ Wb/m^2$. If the acceleration of the rod is $5 \ m/s^2$, then the rate of increase of induced $emf$ is . . . . . . .

$A$ circular coil of radius $10\; cm$,$500$ turns,and resistance $2\; \Omega$ is placed with its plane perpendicular to the horizontal component of the Earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in $0.25\; s$. Estimate the magnitudes of the emf and current induced in the coil. The horizontal component of the Earth's magnetic field at the place is $3.0 \times 10^{-5}\; T$.

The radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of $r_0 \ m s^{-1}$. If at any instant the radius of the loop is $r$,then the emf induced in the loop at that instant will be:

Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side $a$ initially. $A$ uniform magnetic field $B$ exists at right angles to the plane containing the conductors. They all start moving outwards with a constant velocity $v$. If $r$ is the resistance per unit length of the wire,the current in the circuit will be

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

$A$ uniform magnetic field of $0.4 \ \text{T}$ acts perpendicular to a circular copper disc $20 \ \text{cm}$ in radius. The disc is rotating with a uniform angular velocity of $10 \pi \ \text{rad s}^{-1}$ about an axis passing through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim (in $\text{V}$)? $(\pi = 3.14)$