Name the SI unit of magnetic flux and show that it equals volt-sec. Give three possible ways of producing an induced emf in a coil giving an example in each case.

A metallic rod of length $l$ and resistance $R$ is rotated with a frequency $v$, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $l$, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field $B$ parallel to the axis is present everywhere.

Derive the expression for the induced emf and the current in the rod.

A metallic rod of length $l$ and resistance $R$ is rotated with a frequency $v$, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $l$, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field $B$ parallel to the axis is present everywhere.

Due to the presence of the current in the rod and of the magnetic field, find the expression for the magnitude and direction of the force acting on this rod.

A metallic rod of length $l$ and resistance $R$ is rotated with a frequency $v$, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $l$, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field $B$ Parallel to the axis is present everywhere.

Hence, obtain the expression for the power required to rotate the rod.

Figure 6.67 shows an inductor L and a resistor R connected in parallel to a battery through a switch. The resistance of R is the same as that of the coil that makes L. Two identical bulbs are put in each arm of the circuit.

Which of the bulbs lights up bright when $S$ is closed?

Give reason for your answer.