In a Wheatstone's bridge, three resistance $$P, Q$$ and $$R$$ connected in the three arms and the fourth arm is formed by two resistances $${S_1}$$ and $${S_2}$$ connected in parallel. The condition for the bridge to be balanced will be

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

The flux linked with a coil at any instant $$'t'$$ is given by
$$\phi = 10{t^2} - 50t + 250$$
The induced $$emf$$ at $$t=3s$$ is

A long solenoid has $$200$$ turns per $$cm$$ and carries a current $$i.$$ The magnetic field at its center is $$6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}.$$ Another long solenoid has $$100$$ turns per $$cm$$ and it carries a current $${i \over 3}$$. The value of the magnetic field at its center is