The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$. Then the total quantity of electric charge $Q$ which is passing during this time through any point of the circuit is given by:

$A$ coil with $10$ turns and a resistance of $20\,\Omega$ is connected in series with a ballistic galvanometer ($B$.$G$.) of resistance $30\,\Omega$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $10^{-2}\,T$. If it is now turned through an angle of $60^{\circ}$ about an axis in its plane, find the charge induced in the coil $..............\times 10^{-5} \, C$ (Area of the coil $= 10^{-2}\,m^2$).

$A$ bar magnet falls with its north pole pointing down through the axis of a copper ring. When viewed from above,the current in the ring will be

$A$ hundred turns of insulated copper wire are wrapped around an iron cylinder of area $1 \times 10^{-3} \ m^2$ and are connected to a resistor. The total resistance in the circuit is $10 \ \Omega$. If the longitudinal magnetic induction in the iron changes from $1 \ Wb/m^2$ in one direction to $1 \ Wb/m^2$ in the opposite direction,how much charge flows through the circuit?

$A$ physicist works in a laboratory where the magnetic field is $2 \, T$. She wears a necklace enclosing an area of $0.01 \, m^2$ in such a way that the plane of the necklace is normal to the field,and it has a resistance $R = 0.01 \, \Omega$. Because of a power failure,the magnetic field decays to $1 \, T$ in $10^{-3} \, s$. What is the total heat produced in her necklace in Joules?

The magnetic flux through a loop of resistance $10 \Omega$ is given by $\phi = 5t^2 - 4t + 1 \text{ Wb}$. How much current is induced in the loop after $0.2 \text{ s}$ (in $\text{ A}$)?